I just upgraded to the latest version, -36. The problem still occurs, but I would like to quantify my statement.

Sometimes it just works after reboot. The last time I rebooted into -36, it didn't work:

[   27.331188] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   27.528030] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   27.728030] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   27.928030] wlan0: direct probe to 00:21:91:dc:94:57 timed out
[   36.032700] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   36.232028] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   36.432030] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   36.632043] wlan0: direct probe to 00:21:91:dc:94:57 timed out
[   44.940623] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   45.140051] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   45.340044] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   45.540044] wlan0: direct probe to 00:21:91:dc:94:57 timed out
[   61.945281] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   62.144064] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   62.344069] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   62.544064] wlan0: direct probe to 00:21:91:dc:94:57 timed out
[   70.851155] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   71.048040] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   71.248147] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   71.448132] wlan0: direct probe to 00:21:91:dc:94:57 timed out

I then rmmod iwlwifi and insmoded it again:

Then after a few retries, it started working:

[   79.664793] iwlwifi 0000:03:00.0: PCI INT A disabled
[   84.661642] Intel(R) Wireless WiFi Link AGN driver for Linux, in-tree:
[   84.661645] Copyright(c) 2003-2011 Intel Corporation
[   84.661694] iwlwifi 0000:03:00.0: PCI INT A -> GSI 17 (level, low) -> IRQ 17
[   84.661706] iwlwifi 0000:03:00.0: setting latency timer to 64
[   84.661730] iwlwifi 0000:03:00.0: pci_resource_len = 0x00002000
[   84.661732] iwlwifi 0000:03:00.0: pci_resource_base = f845c000
[   84.661734] iwlwifi 0000:03:00.0: HW Revision ID = 0x0
[   84.661819] iwlwifi 0000:03:00.0: irq 44 for MSI/MSI-X
[   84.661861] iwlwifi 0000:03:00.0: Detected Intel(R) Ultimate N WiFi Link 5300 AGN, REV=0x24
[   84.661922] iwlwifi 0000:03:00.0: L1 Disabled; Enabling L0S
[   84.683775] iwlwifi 0000:03:00.0: device EEPROM VER=0x11f, CALIB=0x4
[   84.683778] iwlwifi 0000:03:00.0: Device SKU: 0Xf0
[   84.683802] iwlwifi 0000:03:00.0: Tunable channels: 13 802.11bg, 24 802.11a channels
[   84.687839] iwlwifi 0000:03:00.0: loaded firmware version 8.83.5.1 build 33692
[   84.688113] Registered led device: phy1-led
[   84.688143] cfg80211: Ignoring regulatory request Set by core since the driver uses its own custom regulatory domain
[   84.689366] ieee80211 phy1: Selected rate control algorithm 'iwl-agn-rs'
[   84.701998] iwlwifi 0000:03:00.0: L1 Disabled; Enabling L0S
[   84.705005] iwlwifi 0000:03:00.0: Radio type=0x0-0x2-0x0
[   84.857046] iwlwifi 0000:03:00.0: L1 Disabled; Enabling L0S
[   84.860047] iwlwifi 0000:03:00.0: Radio type=0x0-0x2-0x0
[   84.909114] ADDRCONF(NETDEV_UP): wlan0: link is not ready
[   84.910215] ADDRCONF(NETDEV_UP): wlan0: link is not ready
[   86.730788] cfg80211: Found new beacon on frequency: 5200 MHz (Ch 40) on phy1
[   92.666348] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[   92.864153] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[   93.064230] wlan0: direct probe to 00:21:91:dc:94:57 (try 3/3)
[   93.264175] wlan0: direct probe to 00:21:91:dc:94:57 timed out
[  101.366922] wlan0: direct probe to 00:21:91:dc:94:57 (try 1/3)
[  101.564078] wlan0: direct probe to 00:21:91:dc:94:57 (try 2/3)
[  101.565194] wlan0: direct probe responded
[  101.580086] wlan0: authenticate with 00:21:91:dc:94:57 (try 1)
[  101.580568] wlan0: authenticated
[  101.586846] wlan0: associate with 00:21:91:dc:94:57 (try 1)
[  101.784051] wlan0: associate with 00:21:91:dc:94:57 (try 2)
[  101.785446] wlan0: RX AssocResp from 00:21:91:dc:94:57 (capab=0x111 status=0 aid=3)
[  101.785454] wlan0: associated
[  101.794763] ADDRCONF(NETDEV_CHANGE): wlan0: link becomes ready
[  101.794823] cfg80211: Calling CRDA for country: GB
[  101.801145] cfg80211: Updating information on frequency 2412 MHz for a 20 MHz width channel with regulatory rule:
[  101.801149] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801152] cfg80211: Updating information on frequency 2417 MHz for a 20 MHz width channel with regulatory rule:
[  101.801154] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801156] cfg80211: Updating information on frequency 2422 MHz for a 20 MHz width channel with regulatory rule:
[  101.801159] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801161] cfg80211: Updating information on frequency 2427 MHz for a 20 MHz width channel with regulatory rule:
[  101.801163] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801165] cfg80211: Updating information on frequency 2432 MHz for a 20 MHz width channel with regulatory rule:
[  101.801168] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801170] cfg80211: Updating information on frequency 2437 MHz for a 20 MHz width channel with regulatory rule:
[  101.801173] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801175] cfg80211: Updating information on frequency 2442 MHz for a 20 MHz width channel with regulatory rule:
[  101.801177] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801179] cfg80211: Updating information on frequency 2447 MHz for a 20 MHz width channel with regulatory rule:
[  101.801182] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801184] cfg80211: Updating information on frequency 2452 MHz for a 20 MHz width channel with regulatory rule:
[  101.801186] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801188] cfg80211: Updating information on frequency 2457 MHz for a 20 MHz width channel with regulatory rule:
[  101.801191] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801193] cfg80211: Updating information on frequency 2462 MHz for a 20 MHz width channel with regulatory rule:
[  101.801195] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801197] cfg80211: Updating information on frequency 2467 MHz for a 20 MHz width channel with regulatory rule:
[  101.801200] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801202] cfg80211: Updating information on frequency 2472 MHz for a 20 MHz width channel with regulatory rule:
[  101.801204] cfg80211: 2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801207] cfg80211: Updating information on frequency 5180 MHz for a 20 MHz width channel with regulatory rule:
[  101.801209] cfg80211: 5170000 KHz - 5250000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801211] cfg80211: Updating information on frequency 5200 MHz for a 20 MHz width channel with regulatory rule:
[  101.801214] cfg80211: 5170000 KHz - 5250000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801216] cfg80211: Updating information on frequency 5220 MHz for a 20 MHz width channel with regulatory rule:
[  101.801218] cfg80211: 5170000 KHz - 5250000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801220] cfg80211: Updating information on frequency 5240 MHz for a 20 MHz width channel with regulatory rule:
[  101.801223] cfg80211: 5170000 KHz - 5250000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801225] cfg80211: Updating information on frequency 5260 MHz for a 20 MHz width channel with regulatory rule:
[  101.801227] cfg80211: 5250000 KHz - 5330000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801229] cfg80211: Updating information on frequency 5280 MHz for a 20 MHz width channel with regulatory rule:
[  101.801232] cfg80211: 5250000 KHz - 5330000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801234] cfg80211: Updating information on frequency 5300 MHz for a 20 MHz width channel with regulatory rule:
[  101.801236] cfg80211: 5250000 KHz - 5330000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801238] cfg80211: Updating information on frequency 5320 MHz for a 20 MHz width channel with regulatory rule:
[  101.801241] cfg80211: 5250000 KHz - 5330000 KHz @ 40000 KHz), (N/A mBi, 2000 mBm)
[  101.801243] cfg80211: Updating information on frequency 5500 MHz for a 20 MHz width channel with regulatory rule:
[  101.801245] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801247] cfg80211: Updating information on frequency 5520 MHz for a 20 MHz width channel with regulatory rule:
[  101.801250] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801252] cfg80211: Updating information on frequency 5540 MHz for a 20 MHz width channel with regulatory rule:
[  101.801254] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801256] cfg80211: Updating information on frequency 5560 MHz for a 20 MHz width channel with regulatory rule:
[  101.801259] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801261] cfg80211: Updating information on frequency 5580 MHz for a 20 MHz width channel with regulatory rule:
[  101.801263] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801265] cfg80211: Updating information on frequency 5600 MHz for a 20 MHz width channel with regulatory rule:
[  101.801268] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801270] cfg80211: Updating information on frequency 5620 MHz for a 20 MHz width channel with regulatory rule:
[  101.801272] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801274] cfg80211: Updating information on frequency 5640 MHz for a 20 MHz width channel with regulatory rule:
[  101.801277] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801279] cfg80211: Updating information on frequency 5660 MHz for a 20 MHz width channel with regulatory rule:
[  101.801282] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801284] cfg80211: Updating information on frequency 5680 MHz for a 20 MHz width channel with regulatory rule:
[  101.801286] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801288] cfg80211: Updating information on frequency 5700 MHz for a 20 MHz width channel with regulatory rule:
[  101.801291] cfg80211: 5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A mBi, 2700 mBm)
[  101.801293] cfg80211: Disabling freq 5745 MHz
[  101.801294] cfg80211: Disabling freq 5765 MHz
[  101.801295] cfg80211: Disabling freq 5785 MHz
[  101.801297] cfg80211: Disabling freq 5805 MHz
[  101.801298] cfg80211: Disabling freq 5825 MHz
[  101.801302] cfg80211: Regulatory domain changed to country: GB
[  101.801304] cfg80211:     (start_freq - end_freq @ bandwidth), (max_antenna_gain, max_eirp)
[  101.801306] cfg80211:     (2402000 KHz - 2482000 KHz @ 40000 KHz), (N/A, 2000 mBm)
[  101.801308] cfg80211:     (5170000 KHz - 5250000 KHz @ 40000 KHz), (N/A, 2000 mBm)
[  101.801310] cfg80211:     (5250000 KHz - 5330000 KHz @ 40000 KHz), (N/A, 2000 mBm)
[  101.801312] cfg80211:     (5490000 KHz - 5710000 KHz @ 40000 KHz), (N/A, 2700 mBm)
[  101.885999] cfg80211: Found new beacon on frequency: 5200 MHz (Ch 40) on phy1

So it can be made to work without rebooting the router, but I have to rmmod/insmod iwlwifi to get it working.