This is an upstream issue, not a packaging issue. So please report to upstream LKML or bugzilla and to Realtek maintainers. This is the best way to solve this type of problems. Thanks.

What does dmesg say about r8169 when plugging in and loading the module?

This is the only recent commit I have found that looks relevant (went in after 2.6.31), but it's for a different chip revision.
http://git.kernel.org/?p=linux/kernel/git/torvalds/linux-2.6.git;a=commit;h=daf9df6d8d0f5a4a406632d4da027655d065d3ba

http://vger.kernel.org/vger-lists.html#netdev
netdev is where you want to go and cc:romieu@fr.zoreil.com
http://bugzilla.kernel.org/

I have similar problem, with Realtec card - RTL-8110SC/8169SC. It used to work with 2.6.31, but after upgrade to 2.6.32, it stopped work. Though everything seems to be allright, eth0 is up, no error logs in dmesg or /var/log/*, I compared outputs of ethtool eth0 with livecd - no difference.... Everywhere I looked it seems to be allright.
When I ping some web, most packets are lost, but few manage to get through. I cant ping gateway at all (weird)...
I tried to downgrade to 2.6.31, and it did not work there - thought it used to work for few month with this kernel before...
Only obvious symptom is high number of interrupts in /proc/interrupts for eth0....

I have not find any solution to this so far...

I have similar problem too, whith same chipset.

The only solution I found is to force to 10baseT-FD with mii-tool then re-up the interface. But it sucks... I'm looking for a way to compile the drivers in the 2.6.32 kernel.

mii-tool -F 10baseT-FD
ifconfig eth0 down
ifconfig eth0 up

I have the same problem I think, but only happens when I play Warcraft 3 trought wine, I enter ingame, on battle.net or even a single player game, the eth0 crash and kernel lock if I stay playing longer. I need to reboot to back to normal.
I think the problem maybe correlated to nvidia driver too because only happens here if I play w3 (only 3d game I am playing), I'm using v190, tried v195 too. This problem only begun with december updates here, I have this arch install from begin of 2009 and never got this problem. Already tried changing kernel to .30 .31 .32 and even .33rc4 kernel, but always got the crash, sometimes takes longer to crash (like 20min) sometimes takes 1min.
I could't change to nvidia v185 driver because it needs a prior version of xorg, so it is much trouble...
Tried to reinstall arch too, installed ubuntu and got same problems. Tried the Realtek driver and the crash persist.
And tried with pci=noapic, acpi=off and got same crashes...

This is my crash, I think is nvidia driver related too because of the 2nd line:

RNING: at net/sched/sch_generic.c:246 dev_watchdog+0x1ec/0x200()
Hardware name: GeForce 8000 series
NETDEV WATCHDOG: eth0 (r8169): transmit queue 0 timed out
Modules linked in: w83627ehf hwmon_vid nfs fscache ipv6 nfsd lockd nfs_acl auth_rpcgss sunrpc exportfs ext2 snd_usb_audio snd_usb_lib snd_rawmidi snd_hda_codec_nvhdmi usbhid hid snd_seq_dummy snd_seq_oss snd_seq_midi_event snd_seq snd_seq_device snd_pcm_oss snd_mixer_oss snd_hda_codec_idt nvidia(P) agpgart fan battery usb_storage ac wmi snd_hda_intel snd_hda_codec snd_hwdep snd_pcm snd_timer cpufreq_powersave snd soundcore snd_page_alloc cpufreq_ondemand thermal button powernow_k8 freq_table sg i2c_nforce2 i2c_core processor psmouse shpchp pci_hotplug evdev ohci_hcd r8169 mii ehci_hcd serio_raw pcspkr vboxdrv autofs4 usblp usbcore fuse rtc_cmos rtc_core rtc_lib ext4 mbcache jbd2 crc16 sr_mod cdrom sd_mod pata_acpi ata_generic ahci pata_amd libata scsi_mod
Pid: 0, comm: swapper Tainted: P 2.6.31-ARCH #1
Call Trace:
[<c10464da>] ? warn_slowpath_common+0x7a/0xc0
[<c12807fc>] ? dev_watchdog+0x1ec/0x200
[<c1046597>] ? warn_slowpath_fmt+0x37/0x60
[<c12807fc>] ? dev_watchdog+0x1ec/0x200
[<c106e5c6>] ? getnstimeofday+0x56/0x110
[<c1067821>] ? ktime_get_ts+0x31/0x80
[<c101e522>] ? lapic_next_event+0x22/0x40
[<c1280610>] ? dev_watchdog+0x0/0x200
[<c105381e>] ? run_timer_softirq+0x11e/0x210
[<c10731de>] ? tick_dev_program_event+0x4e/0xe0
[<c104db2f>] ? __do_softirq+0x9f/0x220
[<c1067a73>] ? hrtimer_interrupt+0x1a3/0x250
[<c104dd05>] ? do_softirq+0x55/0x60
[<c104df1d>] ? irq_exit+0x7d/0x90
[<c101f19f>] ? smp_apic_timer_interrupt+0x5f/0xb0
[<c1054543>] ? get_next_timer_interrupt+0x1d3/0x250
[<c10046d5>] ? apic_timer_interrupt+0x31/0x38
[<c1028da2>] ? native_safe_halt+0x2/0x10
[<c100c8fa>] ? default_idle+0x6a/0x150
[<c100cf13>] ? c1e_idle+0xa3/0x110
[<c1002aec>] ? cpu_idle+0x9c/0xf0
---[ end trace 85b7c75960f71918 ]---
r8169: eth0: link down
r8169: eth0: link down

status with latest 2.6.32.5? any link to upstream report about this?

status update on .33 series?

It works fine with the last kernel update, I also updated the driver on windows quite in the same time. I don't know how the problem had been solved...