Engine shut off randomly in drive

So I have a problem with my Honda when in park it can run forever. But when I'm on the road driving the engine will completely shut off without any strange sounds to go with it. It also happens more frequently at a stop while in drive. The lights continue to work when it shuts off. I've changed the alternator and te problem persists. When it stalls out I usually have to wait 20 seconds before it will start again. Also when trying to start it before 20 seconds it makes not sounds what's so ever, no clicking, no rough starting, just silence. I've found that reving the engine at a stop sometimes prevents a stall from happening. Anyone know what's going on with my car? It is an Automatic.