You could check your Applications Event Log to verify that this application is in fact crashing and if it is an App Crash Error will be generated in the log. An "Application Stopped Working" should also appear in the Action Center Reliability Monitor. You could also see if you have the current version. With HP Support Assistant open click on the About Tab in upper right and you can check for a newer version.
HP Support Assistant is a problematic program. The HP Support Forum is loaded with posts from HP users that have problems with this program.