I've had a number of PEAKs fail - fail to escape from Lightnappers, with the result that my collection has been slipping away light by light. I attribute part of this to my fondness for polished brass PEAKS.
As for LiIons, which I now use almost exclusively (except in the 2 X AAA and 2 X AA bodies), none of my PEAKs have been damaged or, so far as I can tell, affected in the least by heat. Having discussed this at length with Curt - who knows infinitely more than I about this subject - it appears that failures will more likely be in the form of a gradual degradation of performance as the LED phosphor coating is slowly eroded by heat. But the design and build of these lights has been enhanced by the use of a heat-transfering epoxy which surrounds the heatsink and which certainly seems to work well in drawing the heat away from the LED and circuitry.
Before PEAK's Eigers appeared on the scene, Curt advised that running LiIons with 5mm's would significantly reduce LED lifespan. However, the 5mm's and P'4s in my many PEAKs have not suffered in the least from LiIon heat. Time will tell about the Rebels in the Eigers. If any heat related problems do develop I suspect that it would be principally due to the smaller mass of the Eigers and perhaps due to the lower heat-transferring efficiency of SS and Brass bodies that are so popular. If any such problems are reported in the future, we can switch over to HAIII's, or Eneloops, or just ignore them.
Other types of failures? I've had none at all, which seems to me to be the result of phenomenal engineering and the careful way in which PEAKS are built. I am fortunate enough to live nearby, have witnessed first-hand the manufacturing and assembly process of these lights, and am truly impressed with their quality. There is, of course, room for improvement: MORE BRASS and MORE KNURLED SS!