Noise, particularly from ever-more-present electronics, is what's killing AM radio.
One reason people originally gravitated to FM - and its entire raison d'être - was freedom from noise. For the longest time, though, that meant specialty formats, such as classical programming, were what drove adoption. After the dark days of the 1950s, FM started growing again, thanks to the adoption of stereo programming (not a part of FM originally) and the adaptation of more popular formats more attuned to shifts in taste. In more concrete terms, people started getting tired of screaming Top-40 jocks and constant patter and commercials and gradually shifted to FM.
Honestly, high-power operation isn't going to save AM - it certainly hasn't in Europe - and low-power operation isn't going to either - the experience with it in the Netherlands is very mixed and many of the LPAM stations there are having a rough go of it.
Nor should FM stations be complacent - HD isn't going to save FM, even though it does a decent job of solving problems with multipath - and the programming on many stations doesn't provide the kind of experience that many listeners are now looking for.