At my company, we use a hand-rolled AJAX solution (it's about 2-3 years old, otherwise we probably would have used someone else's solution).  Recently, we've applied it to one of our secure (HTTPS) websites and we've been having intermittant problems with the XMLHTTP object on the browser (always IE 5.5+) sending requests to the server (always Win2k3).  It happens about once every 20-25 requests and just returns an error message that says "The download of the specified resource has failed."  We tried moving our web service to an HTTP server rather than an HTTPS server and the problem went away, so we're fairly certain that it's a problem with the XMLHTTP object communicating with the secure server, and we've tried stripping out all irrelevant code, so we're also fairly certain that it's not something unrelated. 

We've contact Microsoft support about this and they've confirmed that we're not the first people to encounter this problem but haven't gotten any more info from them yet (although we should hear back soon).

This is just an FYI for those of you jumping on the AJAX bandwagon from someone who's been doing this sort of thing for a while now.