Thomson TG585v8, Broadcom Wireless card, Linux -- anybody else have trouble?

[#1]

My ageing Dell desktop (with  Broadcom wifi adapter) has coexisted fairly happily with my  Thomson 585v8 router since I got the 8.2.7.8 firmware, though it does have a tendency to randomly disappear from my home network. This week, I installed a Ubuntu (12.04) linux partition, which works fairly well -- except that the relationship between the desktop and the router has gone seriously downhill. Two or three times a day, when running Linux, the computer simply drops offline and usually can't get back on, despite repeatedly asking for the password. until I restart the wireless at the router. (That undocumented button on the front comes in handy there!) The router event logs don't have any record of these events, and the signal at the computer is adequate; the problem was occurring even with the router sitting right next to the computer.
So, I was wondering whether anyone here has had similar problems and can suggest anything I could tweak, either in the router settings or the computer, to get better performance? Or would I be better off with a different router? Running on wired ethernet isn't really an option here.

[#2]

A wifi adapter from a company with better Linux support would have been better.
Disabling power saving  on the wifi adapter with "iw dev wlan0 set power_save off" might help.

[#3]

Thanks! I'll try that and see how it goes.
I didn't know when I bought the machine five years ago that I was going to want to try Linux on it.  The only spare wifi adapter around here is an ancient Netgear WG111 dongle, and a quick Google suggests that isn't exactly linux-friendly either.