After about 30 min of mowing the mower starts acting like it’s gonna cut off. Where do I look first?

SOURCE: cuts out and stops sometimes after 30 min. or so

check your fuel delivery system. It sounds like a blocked filter, failing pump or a restriction in the fuel line. 

SOURCE: 15.5 horse craftsman riding mower. Runs fine

carb is probaly dirty

SOURCE: mower keeps cutting off

my brother had the same problem with same mower. he took it to service station new plugs etc. still did it he took his back maybe problem with the magneto/ coil since you only have 12 hours on it, take it back and get a different make ie john deere or cub cadet husqvarna riders are junk!!!!!

SOURCE: Mower stops running after I've been mowing for

Mower stops running after mowing about 5 minutes. acting like it was running out of gas unitl eventually stops. I wait 10 minutes and then it restarts, runs good, then erratic...then quits again?

SOURCE: My parents have a self

Does the mower die right away (cuts out) or does it sputter to a halt. Sputtering out would indicate a fuel problem. If it just cuts out when hot, then more likely an ignition problem. Your coil may need replacing. Take a close look at the coil wire (spark plug wire) and its routing. Make sure it's not touching part of the engine where it's heating up and has caused a "leak" to ground it out when it gets hot. If all is well then check your spark when the engine is hot and cuts out. Make sure you have a very good blue spark and not a weak one (check it cold first and then compare!). Again, indicating a possible ignition coil problem. Hope this helps and best of luck to you.
James