For what it's worth...
I used to pick up a lot of Linksys BEFSR41's for friends and clients, but I stopped early this year because maybe a third of them (like 6 or 7 out of the 20 or so) ended up with problems like Canadian Bacon is describing. (That is... they'll be working along, and then they'll stop routing traffic, or the router's DNS will break.)
Common symptom... Traffic to the outside world ceases, you can still use http to hit the router's administrative functions... Do a DHCP release and get all those pretty 0.0.0.0's, but then try a DHCP renew... and the router goes off into the weeds and leaves you sitting there watching your browser's activity indicator spin around. Then when you get tired of waiting for nothing to happen, you can power cycle and everything'll be ok for a little while.
Running a p2p application may or may not cause it to barf more quickly (but if you don't limit your connections, chances are you'll have more problems). Running a hell of a lot of UDP packets (many games, xbox live) may or may not cause it to malfunction more quickly. Firmware upgrades don't seem to matter.
I've had access to a lot of BEFSR41's and my experience is if your system is behaving like this, chances are it's not a power supply (transformer) issue. (Multiple power supplies tested on both misbehaving and righteous BEFSR41's.) fwiw, I've seen fewer problems on v2 models, but they still have 'em.
As for what to do about this...
Can't hurt to upgrade the firmware, but I doubt this will fix anything.
If your BEFSR41 is just losing its ability to provide dns (symptom: currently existing connections are maintained, new connections specified to a dotted quad can be made, but new addresses can't be resolved), you can set your computer's DNS to the outside address instead of to the router (192.168.1.1 by default).
However, if your BEFSR41 simply stops routing traffic... If you're running a p2p app, you can cut down on the number of total connections to just a couple hundred to see if it helps. Otherwise if it keeps hanging every so often, I'd replace it.
My choice of replacements has been to either use a spare computer for a router (see freshmeat.net) or go with the DLink DI604. I'm not crazy about DLink, and lord knows the older DLink's had some f'd up non-working firmware, but for what most people do, they work ok now and they're cheap ($40-$50). I'm not sure how well the DI604 works with P2P though...