I’ve just upgraded my WRT54G firmware to v3.03.6 HyperWRT_2.1b1 created by Timothy Jans. Previously, with the default firmware provided by Linksys (v3.03.6) the router frequently hangs. Now, it is rock stable.
Read more about this firmware at http://www.hyperwrt.org
As I search for the solution of the problem, I also stumbled upon a great site, dedicated to the particular router: http://www.wrt54g.com
Kudos to Timothy Jans!