Chances are that the PTC component has failed. This essentially controls the degauss-on-startup behavior. If it's bad, the degauss coil either will always be partially on, won't run at full strength when it's supposed to, will run for a longer/shorter time than it should, etc. Any of those could cause the behavior you're seeing. Generally it's easy enough to replace if you can identify your monitor and are willing to swap a component on the board out.