My car just started running rough in the Morning.

My car just started running rough in the morning when started then smoothes out after a few seconds. The main problem is it will drive fine for about 10 miles or so then start to cut out (RPMs fluctuate but ultimately go down) even if I push on the gas it will continue to die down untill it either dies or I stop and turn it off. After about 10 min of sitting it will start up and go for a little while longer untill the same thing happens again. I've replace the fuel filter and the purge valve solenoid. Help please