Did you try cleaning your power switch? It's problematic on SP's and could be the culprit of your intermittent power.
https://www.ifixit.com/Guide/Nintend...lacement/12889
http://forum.digitpress.com/forum/sh...=1#post1993217
My backlit SP has symptoms just like yours with one addition. Oftentimes when sliding the power switch to the on position, the system will start for a split second and immediately turn off, forcing me to slide the switch down and try again. Otherwise, my issues are identical.
Frustrating for what is a very lightly used system that I bought new. Need to tackle the problem one of these days.