Sounds similar to an issue I'm having. I noticed from the begining that my Wifi Speeds (using the Speedtest app) were horrible when compared to my iPhone. I didn't pay that much attention because it was still decent speed for a phone. However, when I noticed that WiFi was one of my biggest battery drainers I started digging a little deeper.
It seems like my Wifi connection is dropping when there are bursts of data. For example, if I use the speedtest app repeatedly (or use the speedtest tools on dslreport.com) I'll quickly get to a point where my data connection is hosed (the speedtest app will complain about losing network connectivity, web browser will indicate that there is no internet connection). It doesn't seem to completely drop the connection, but Wifi is definitly vey flakey with the combination of the Bionic and my network (which is nothing fancy, just using WPA2 for security)
I'll certainly try forgetting the network and then reentering the credentials (thanks for that tip) but if wifi is not rock solid, I can't see keeping a very expensive phone and then hoping the issue is fixed with a firmware upgrade.
I'll post back if I find anything that works