EDITED - See my last post to avoid confusion.

Try going to the blower motor and tapping it see if it moves when it not working. If does work the blower motor is bad.

sounds like th blower motor has an intermittant short or an open coil in the windings.. causing random circuit failure and power drops

Do you have climate control, or manual heating & cooling? If you have climate control another potential problem could be the fan control module. If you have manual, it could be the resister pack which regulates fan speed. Or like mentioned above the fan itself could be at fault.

EDITED

EDITED

I'm gonna second (third? more?) the blower motor. First, it'* the easiest fix and secondly, most probable. The resistor pack, in my mind anyways, just wouldn't act the way you described the issue

I recently had the same problem please if you find a fan motor and the part number, please let me know, I need a new one as well.. even thru junkyards, or internet..
I also put my thread just now and I saw yours I hope you fix it, I'll let you know If I do.

Thanks,

could be the felt on the end of the blower motor is wore tap it ,chech it is fully plugged in........on firewall under hood.....a quick fix is to drill a hole in the top of the nipple of the fan and put a couple drops of oil in it and it will work

EDITED