Ok, I would start by checking the power at the high speed fan relay on the A/C box under the hood. It could be opening up under heat and load, OR it is losing power feed to it.
If I remember, there is a separate fuse dir for high speed. I have seen the fuse lose connection to the terminal in the fuse panel, but could be elsewhere.
Also, check the motor ground.
If it stays running on the lower fan speeds, you shouldn't have a blower motor problem.