I also have this problem on my Gateway MX6440. I did not have this problem in 6.10, the card reader worked fine with tifm_sd / tifm_7xx1, tifm_core (and mmc_core). In order to get it to work with the 6.10 live cd I simply have to modprobe tifm_sd and it works.

On 7.04 it used to work occasionally. My 7.04 was an upgrade from 6.10 with a working configuration for the sd card reader, to which I had added  tifm_sd, tifm_7xx1, tifm_core to /etc/modules. When the bug happened, /etc/modules did not have any ti* in it. Occasionally, (maybe 10-20%) if I started the computer up with the card in it or just inserted the sd card it work work and everything would be fine. The rest of the time nothing would happen that I could tell from the GUI. I realized today that my /root (because I didn't make a separate /var when I installed on my laptop) is full and I am unable to log in to my system. My /var directory contains aprox 18GB of logs, mainly in syslog.0 kern.log.0 syslog kern.log messages.0 messages all of which are 1-4.2GB in size. These huge logs were created in past 36-48 hours as my SO had left the SD in the laptop which was kept running the whole time.

This is an excerpt from /var/log/syslog

[133611.664000] tifm_sd: card failed to respond for a long period of time<6>tifm_7xx1: demand removing card from socket 3
[133611.664000] mmcblk0: error 1 sending read/write command
[133611.664000] end_request: I/O error, dev mmcblk0, sector 990912
[133611.664000] printk: 1277 messages suppressed
[133611.664000] Buffer I/O error on device mmcblk0, logical block 123864
[133611.664000] mmcblk0: error 1 sending read/write command
[133611.664000] end_request: I/O error, dev mmcblk0, sector 990912
[133611.664000] Buffer I/O error on device mmcblk0, logical block 123864
 
lspci -vv says

05:09.4 Class 0805: Texas Instruments PCI6411, PCI6421, PCI6611, PCI6621, PCI7411, PCI7421, PCI7611, PCI7621 Secure Digital (SD) Controller
        Subsystem: Gateway 2000 Unknown device 0300
        Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B-
        Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=medium >TAbort- <TAbort- <MAbort- >SERR- <PERR-
        Latency: 64 (1750ns min, 1000ns max), Cache Line Size: 32 bytes
        Interrupt: pin A routed to IRQ 177
        Region 0: Memory at d0309000 (32-bit, non-prefetchable) [size=256]
        Region 1: Memory at d0308c00 (32-bit, non-prefetchable) [size=256]
        Region 2: Memory at d0308800 (32-bit, non-prefetchable) [size=256]
        Capabilities: [80] Power Management version 2
                Flags: PMEClk- DSI- D1+ D2+ AuxCurrent=0mA PME(D0+,D1+,D2+,D3hot+,D3cold-)
                Status: D0 PME-Enable- DSel=0 DScale=0 PME-

05:09.3 Mass storage controller: Texas Instruments PCIxx21 Integrated FlashMedia Controller
        Subsystem: Gateway 2000 Unknown device 0300
        Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B-
        Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=medium >TAbort- <TAbort- <MAbort- >SERR- <PERR-
        Latency: 64 (1750ns min, 1000ns max), Cache Line Size: 32 bytes
        Interrupt: pin A routed to IRQ 177
        Region 0: Memory at d0306000 (32-bit, non-prefetchable) [size=8K]
        Capabilities: [44] Power Management version 2
                Flags: PMEClk- DSI- D1+ D2+ AuxCurrent=0mA PME(D0+,D1+,D2+,D3hot+,D3cold-)
                Status: D0 PME-Enable- DSel=0 DScale=0 PME+

I will try the fixes above and report back soon if they help. The major issue here for me wasn't that it didn't work, but that the logs put my machine in an unusable state. While its not a difficult fix for me, and shame on me for not making /var a separate partition. IIRC the installer doesn't make a separate /var by default, so its possible that this could happen to other people as well.