I have been having the same problems with Vegas Pro 14. Depending on what video card you have (or maybe it doesn’t matter) I was able to bump up the fan speed (Radeon RX 480 video card) and put a small fan to blow on the computer.
Because it would just stop like you said, I had the thought it was heat related. I may be wrong, but on the third try with the fan on the video card at +3000rpm and an external room fan blowing fresh air supply to the computer case it make it thru. My video was over 20 minutes long. I also never had this problem before and have been using Vegas since version 11.
I have learned I need a back-up, or another possible program since I need to make quite a few videos and have started to learn DiVinci free version. It is a tough change, and Vegas just does things so much easier, but I don’t see a lot of “spark” or even communication from the company about the future of Vegas. They stay totally silent, and that makes my uncomfortable.
Peter