Realtek lists the driver version number as 1086.7 dated January 27th 2010 it doesn't say specifically 32bit or 64 bit, but I suspect it includes both. Check and make sure that is the version number you are using.
There is also a firmware update for that router dated March 13th 2009, not sure if that will help or not, generally a good idea to run the most current firmware but a bad update can pretty much brick the router, so follow the directions carefully and only attempt to perform the update with a wired connection.
Since the linksys wireless dongle link you provided shows that it is compatible with both 32bit and 64bit versions of Windows7 then I would suspect a potential router issue.
However, if you suspect a problem with a system...