Did you use an aftermarket starter? They just aren't as good as the Nissan OEM starters. It may be starting to give up the ghost. Just for giggles, make sure your battery cables are in good shape, are clean, and are tight. Also make sure the starter solenoid wire is clean and tight. If the problems continue, pull the starter and see what kind of shape its in. If the gears are all ground down, or things seem loose and sloppy, send it back where you got it for a warrantied replacement.

It could be something else, I guess, but off the top of my head, I can't think what. Neutral safety switch? Don't know. Never had an automatic. Maybe others have had your problem before, and will post their solution.

 

Could very well be the starter teeth are wearing down OR the teeth on the flywheel. Just moving it a bit may be allowing the flywheel to move just enough to let it 'engage'. That's if it's a fairly loud 'huummmmm' when you crank as if the starter motor is turning but nothing else is happening. Also just might be the solenoid isn't throwing the gear onto the flywheel. But overall it sounds like a starter going bad. Aftermarket uhhhhh,,,,, big box store starters may have a 'lifetime' warranty but sometimes you need to keep having the warranty fulfilled! Sort of like the aftermarket alternators. Sometimes they're good, sometimes they're basically a 'repaint'!