We've seen some issues with IE6 and POSTing via SSL. Here's some further info: http://www.modwest.com/help/kb2-260.html
Applying the MS patch to the browser fixes the issue. Another way to check if it is browser specific is to use another browser (Firefox?) and see if the behaviour is the same.
There should be little difference if booster is running on SSL or not. The HTTPS encryption happens at the socket level long before Booster gets hold of the data. Internally, nothing unique happens to a secure connections.