Having worked for a company manufacturing heated pitots that was bought by Goodrich, I accept that pitot heaters can fail, but what are the chances of three failing in a short period, all three would have been working at takeoff, it seem to me to be extremely unlikely that three would fail at once, they would likely be from different manufacturing batches.
What about
extremely damaging hail or so much hail that the heater(s) couldn't keep up with the ice jamming up the orifices?