Pegasus Mail might be minimizing to the Notification area.  Win7 hides icons in the Notification area so click the "Show Hidden Icons" triangle and see if the Pegasus Mail icon is there when it it minimized.

You might want it to minimize to the taskbar instead.  If so, go to Tools > User interface > Reporting/logging and unselect the "Hide the Pegasus Mail taskbar entry when minimized" option.

Maybe asked before, but I couldn't find it:

Just migrated Pmail from old XP to Win 7 Pro/64.  Open Pegasus, and all seems well. But after minimizing to do something else, it just disappear, and won't reopen. 

Find that process is still running. Kill process. and opens again, not without complaint. Something isn't set right.

Any thoughts appreciated.