jd 160 riding mower dies out after running for awhile?

my jd 160 will start up fine and run fine for 5-20 min. and then will die out and stall. It will then start back up but will run rough for a few min. if i let it sit for awile it can then be started up and run for 5-20 min again. Have changed the fuel filter, pump and have a new gas cap. Any suggestions?