Wow, nice mess. I have a BEFW11S4v4 on my desk. Works well enough with a few bugs.
It would be interesting to know if only the channel settings are not sticking, or if other settings on the same page have a similar problem.
Apparently only the wireless settings are not being held. I've actually seen problems like this, but it wasn't the router. It was the cache in the browser insisting on displaying the expired web page instead of displaying the current changes to the web page. The changes were being applied, but the browser would display the page from the browser cache, not from the router.
Instead of fixing the problem, it would be interesting to see first if I'm correct. Setup your system to change the wireless settings as before. Change the channel and click apply. Restart the router (power cycle). Then, using a wireless client monitoring program or Netstumbler, see what channel your router is really using. If my guess(tm) is correct, then it should have changed, even though the web page shows that it has not changed.
I also had trouble configuring Linksys devices using alternative browsers. The major culprits were Opera and old Netscrape 4.7x versions. Early also Mozilla releases did strange things. However, I don't recall if any were cache issues. More like Javascript or HTML bugs. Sorry, it's been a long time, so I don't recall the exact problems. I do vaguely recall where clicking on some button did nothing, as if the button wasn't there. I also found I couldn't use the web based firmware upgrade with Netscape or Opera. Anyway, when I reluctantly switched to Internet Exploder 6, things worked.
Firmware release notes: