I just brought this thread up searching for something similar.
I too have a BEFW11S4 at this house and my roommates and I get disconnected a lot.
I wanted to upgrade the firmware but it comes factory loaded with 1.50.14, apparently the newest, and this router is at least 1.5 years old. Way to support the product! :\
Upon looking into this further, it seems there is a 1.52.02 that is out (i seen several threads of people with BEFW11Sv4 with 1.50.14 and some with 1.52.02) EVEN THOUGH Linksys does not appear to host it on their website. I was able to find it from opendrivers.com, but there didn't seem to be much official mention of it at all. What is going on here and that also leads to the question on why are there so many threads of people with ONLY this router having these problems?