Repairs Walk behind Mower

I have a John Deere Self Propelled walk behind mower [JS40.] The mower starts right up runs fine then stalls after about 5 minutes and will not restart. I replaced the carburetor thinking it was picking up dirt but it still did the same thing. It seems to be related to the mower getting to operating temperature. Am I looking at a bad magneto or coil and loosing spark?
Thanks

Get an inline spark tester to check and see if you are loosing spark.