"I was told it does the typical shut down after 15-20 minutes then when it sits for a few it fires back up for a short amount of time"
Typical? Don't think so.
Check fuel cap vent. Replace fuel filter.

Briggs OHV engines require proper valve lash for the compression release to function.

Did you LOAD test the battery? If you didn't, you don't know how good it is or isn't.
You can try jumping the 2 large studs on the starter solenoid. IF the engine cranks, battery & starter are good.

BTW- Posting the Sears 917.xxxxxx number is useful so we can see EXACTLY which tractor you have.

This post was edited by bill_kapaun on Mon, Dec 16, 13 at 9:17

Agree with Bill. Adjust valves for the no start problem and run it with the fuel cap off (On but very loose so air can get through the grooves) to see if poor gas tank venting is causing the 20 minute shut down.

There is no typical 20 minute shut down. Any company that would build a mower like that would end up having a typical factory shut down.