I had an issue once on a High Speed where the flipper would lock on and release in a similar way. The switch in the cabinet was so old and corroded it would literally stick together and pressing the button a few times would usually loosen it up and it would separate again so I replaced the switch. Try watching the switch in the cabinet when you press the flipper button in and see what happens.

If you are pulling the coil connector off it makes sense the flipper would de-energize. Did you actually test the diode? If it's happening periodically I would suspect the diode or the leaf switch in the cabinet sticking or making contact somehow as you mentioned pushing the button will also release it.