The fastest way to lose the "flow state" is to, in your words: push it to greater depth.
The flow state is perfect in itself. The key is to be able to experience it at will. Look at any athlete. Some days they're on and some days they're off. The best are on most of the time.
The best way to experience anything desirable is to, according to Jose Silva, go into an alpha bw and relive the experience as soon as you can after experiencing it.