Why is my dryer turning off mid-cycle and staying off for 30-60 minutes?
Yes, Check the vent pipe all the way to the end where it exits the building. You will most likely find that it is stuffed with lint to the point of restricting the air flow from the dryer to the outdoors. Restricted air flow will cause the inside of the dryer to overheat and then some type of safety cutout or thermal breaker is opening up the power circuit. The 30 to 30 minutes you are seeing is likely the time it takes for things to cool back down enough for the thermal cutout to reset itself.

If the vent pipe is clear you should feel a nice brisk flow of warm damp air coming out the end of the dryer vent. 

I had this problem when I moved into my house. Some 15 feet of vent pipe was totally stuffed and I had to do a major amount of unstuffing and running a rotary brush up the pipe on a flexible shaft. I also ended up adding a new larger style vent end flap on the pipe on the side of the house wall that integrated a removable plastic grille. Now I just have to look at that once every 3-4 months and get up there and clean it out.