Hello,

Apologies for the late reply. Been really busy and not had much time for computer troubleshooting recently.

My device is:
Bus 009 Device 003: ID 174c:5136 ASMedia Technology Inc. 

Here's my system information:
System:    Host: BOB1 Kernel: 3.19.0-26-generic x86_64 (64 bit, gcc: 4.8.2) 
           Desktop: Cinnamon 2.6.13  Distro: Linux Mint 17.2 Rafaela
Machine:   System: Gigabyte product: N/A
           Mobo: Gigabyte model: 990FXA-UD3 version: x.x Bios: American Megatrends version: F2 date: 07/15/2013
CPU:       Octa core AMD FX-8350 Eight-Core (-MCP-) cache: 16384 KB flags: (lm nx sse sse2 sse3 sse4_1 sse4_2 sse4a ssse3 svm) bmips: 64286.7 
           Clock Speeds: 1: 1400.00 MHz 2: 1400.00 MHz 3: 1400.00 MHz 4: 1400.00 MHz 5: 1400.00 MHz 6: 1400.00 MHz 7: 1400.00 MHz 8: 1400.00 MHz
Graphics:  Card: NVIDIA GK106 [GeForce GTX 660] bus-ID: 01:00.0 
           X.Org: 1.15.1 drivers: nvidia (unloaded: fbdev,vesa,nouveau) Resolution: 1680x1050@59.9hz, 1680x1050@59.9hz 
           GLX Renderer: GeForce GTX 660/PCIe/SSE2 GLX Version: 4.5.0 NVIDIA 346.72 Direct Rendering: Yes
Audio:     Card-1: NVIDIA GK106 HDMI Audio Controller driver: snd_hda_intel bus-ID: 01:00.1 
           Card-2: Advanced Micro Devices [AMD/ATI] SBx00 Azalia (Intel HDA) driver: snd_hda_intel bus-ID: 00:14.2 
           Sound: Advanced Linux Sound Architecture ver: k3.19.0-26-generic
Network:   Card-1: Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller 
           driver: r8169 ver: 2.3LK-NAPI port: b000 bus-ID: 05:00.0
           IF: eth0 state: down mac: 74:d4:35:5e:c0:be
           Card-2: Ralink RT2800 802.11n PCI driver: rt2800pci ver: 2.3.0 bus-ID: 04:06.0
           IF: wlan0 state: up mac: 68:7f:74:e2:0f:a4
           Card-3: Microsoft Xbox 360 Wireless Adapter usb-ID: 007-004
           IF: N/A state: N/A mac: N/A
Drives:    HDD Total Size: 6501.3GB (20.6% used) 1: id: /dev/sda model: WDC_WD10EADS size: 1000.2GB 
           2: id: /dev/sdb model: WDC_WD20EARS size: 2000.4GB 3: USB id: /dev/sdc model: SNA size: 500.1GB 
           4: USB id: /dev/sdd model: 2105 size: 3000.6GB 
Partition: ID: / size: 25G used: 17G (70%) fs: ext4 ID: /home size: 731G used: 660G (96%) fs: ext4 
           ID: swap-1 size: 4.36GB used: 0.00GB (0%) fs: swap 
RAID:      No RAID devices detected - /proc/mdstat and md_mod kernel raid module present
Sensors:   System Temperatures: cpu: 25.5C mobo: 41.0C gpu: 0.0:51C 
           Fan Speeds (in rpm): cpu: 997 fan-2: 0 fan-3: 0 fan-4: 0 fan-5: 0 
Info:      Processes: 250 Uptime: 5 min Memory: 1708.8/16012.9MB Runlevel: 2 Gcc sys: 4.8.4 
           Client: Shell (bash 4.3.11) inxi: 1.9.17 

Also here's the kernel logs produced when the device is connected:
[  237.728033] usb 2-1: new SuperSpeed USB device number 2 using xhci_hcd
[  237.744780] usb 2-1: New USB device found, idVendor=174c, idProduct=5136
[  237.744783] usb 2-1: New USB device strings: Mfr=2, Product=3, SerialNumber=1
[  237.744785] usb 2-1: Product: AS2105
[  237.744786] usb 2-1: Manufacturer: ASMedia
[  237.744788] usb 2-1: SerialNumber: 00000000000000000000
[  237.745252] usb-storage 2-1:1.0: USB Mass Storage device detected
[  237.745413] scsi host9: usb-storage 2-1:1.0
[  238.744785] scsi 9:0:0:0: Direct-Access     ASMT     2105             0    PQ: 0 ANSI: 6
[  238.745159] sd 9:0:0:0: Attached scsi generic sg4 type 0
[  247.037740] sd 9:0:0:0: [sdd] Very big device. Trying to use READ CAPACITY(16).
[  247.037913] sd 9:0:0:0: [sdd] 5860533168 512-byte logical blocks: (3.00 TB/2.72 TiB)
[  247.038367] sd 9:0:0:0: [sdd] Write Protect is off
[  247.038372] sd 9:0:0:0: [sdd] Mode Sense: 43 00 00 00
[  247.038837] sd 9:0:0:0: [sdd] Write cache: enabled, read cache: enabled, doesn't support DPO or FUA
[  247.039353] sd 9:0:0:0: [sdd] Very big device. Trying to use READ CAPACITY(16).
[  247.121247]  sdd: sdd1 sdd2 sdd3 sdd4 sdd5
[  247.122345] sd 9:0:0:0: [sdd] Very big device. Trying to use READ CAPACITY(16).
[  247.129975] sd 9:0:0:0: [sdd] Attached SCSI disk

My motherboard has a VIA VL805 chip for the USB 3.0 ports, so Intel is not a factor for me. Again, I'm pretty sure that my problems have stopped appearing but I can't be certain until I do a proper test. I'll do some testing tomorrow and report back.