I have a troy bilt riding mower and when I'm going along cutting grass the mower just stall out. When I try to start it, it turns over but won't start, when I turn the key again it just clicks, I turn the key again and again it just clicks, finally I turn the key again and it starts, runs for awhile and stalls out again, and the same thing over again. I replaced the battery in the beginning of the season. What could be wrong now?

Well I don't know the time frame in between it starting again, if it is say about 30 minutes, you could have a coil going bad. If it is to where it is restarting finally within a very short period, I would say you have a naked wire causing a short and killing the engine, then as you are pulling on the rope the vibration may be getting the wire to where it does not touch any metal surface and will restart. Please provide more details if you need more assistance.

There are a couple very simple steps to do here.
1. Install a clear plastic fuel filter. When running you will see fuel in the filter. If you have a fuel issue you will see the filter go dry when it stalls.
2. Try to start the hot engine on full choke. If it starts on full choke but dies when you un-choke it, you have a fuel / carburetor issue.
3. Get a spare spare plug, remove the plug wired from the one in the engine and connect it to the spare. Make sure the threaded body of the spark plug has a good ground. You can use a jumper with alligator clips. Crank the engine and look for a blue spark. You need to do out of the sun and best done in the dark. If spark is weak on missing you have an electrical issue i.e plug or coil etc.