This is indicative of some sort of certificate problem. Check to make sure the machine that provides root certificates is up and running and accessible to FogBugz.
Ideally you'll want to fix the CA machine's issues, but you can circumvent the issue by modifying the sURL registry value in HKLM\Software\Fog Creek Software\FogBugz\[path_to_fogbugz] to use http instead of https. All the heartbeat.asp URL ever returns is a +, - or error message.
In my case I fixed this issue by removing Internet Explorer Enhanced Security Configuration after IE8 was installed. My certificates were showing up as valid in IE and I could navigate to the main fogbugz page but kept getting cert errors in the log. Removing this IE function fixed it for me. It can be removed from the Add/Remove Windows Components in Add or Remove Programs in the Control Panel