Kenmore gas dryer will not start after drying a couple of loads, but will restart after letting it sit for about an hour.

Sounds like the motor is overheating and probably needs to be changed out.when was the last time you cleaned out the dryer and how old is it?the dryer should be taken apart and cleaned out once a year if it's gas and once every two years if it's electric.there's an open flame in a gas dryer and i've seen the lint catch fire in some of them.you should clean out the outside vent,if the vent line is a long run from the back of the dryer to the outside vent i use a leaf blower to blow out the line,clean out the duct that the lint filter slides into and with a shop vac i blow out the motor and vac out the cabinet where the motor is and blow out the gas tube,the lint builds up on the dryer motor,overheats it and all the oil in the motor dries up,you can see it on the back of the drum and around the motor,you'll see lint stuck onto the back of the drum stuck in the oil and like a yellow stain on the frame and wall where the motor is and the motor starts overheating and cuts out when it gets hot,when it cools it will start again but one of these times it wont start at all.sometime you'll hear a loud buzz when you try to start it.the motor is easy to change,you need to decide if you want to put money into the dryer or change it out,good luck