Car will run then die and not turn over

So my sonota will start and run and I can drive. But as soon
as I stop then try to take off again it dies. But after it dies I
can no longer turn it over. It will not engage the starter at all. I
have a new alternator and my battery is still good. It will not
turn over with a jump box or cables hooked up to it. And by
turn over I mean the starter won't even click or engage. It acts
like there isn't juice going to it. But there is. I will let it sit for a
day. And go out and it fires right up like nothing ever was
wrong. It does run rough though. But will then die and repeat
process. So I'm curious what's causing it to do this