This is a fairly common problem and it seems to get worse when it gets hot outside. After a while the lawn mower will restart and then you can mow for a while and then the same thing happens over again.
The most likely culprit here is that the ignition system is heating up and then breaking down inside. When it breaks down, it will cause the ignition coil to stop producing spark and thus the engine dies.
When your engine does die, test for spark by installing an inline spark tester and then cranking the engine. If you do not see any spark, you can assume that your ignition system is at fault. Further testing will need to be performed to narrow down the issue. You will need to know if it is the engine or the machine kill system. You can isolate this by disconnecting the kill system and then checking for spark.
If you need technical assistance with your lawn mower that dies, visit our Locations page to find a shop near you. Professional lawn mower repair companies are available to help.