blower fan on vehicle will sometimes intermitantly shuts off, but the comes back on again in all ranges of time. recently on a hot day it shut off for a day. that night I checked all the fuses, they were fine. next day the fan worked. seems to do this in the winter also.
Start by just pulling the power connector and inspecting it for corrosion or dirt or breaks, etc. You might just be heading for the need for a new motor.
The next time the blower motor stops working, pull over somewhere, reach under the passenger side of the dash and tap on the blower motor with the handle of a screwdriver. If this gets the blower motor operating again the blower motor requires replacement.