The ImageReflector mirror I bought a year or so ago is now bowed, giving a slightly distorted image. It's been in a case in my car all that time, so no physical abuse, but some high temperatures (I park outside in Los Angeles about one day a week in summer).

The "compact case" idea seems promising to me (and I see someone beat me to it). That way you can get one or two glass mirrors, with excellent reflectivity and no distortion, but the case (especially if somewhat resilient, like polyethelene plastic or rubber) keeps the glass from breaking. Ideally, one of the mirrors is slightly magnifying, for the eye, etc., and one not (for the back and other inaccessible areas.) I haven't found the perfect compact online, though - the one here, while possibly suitable, has a minimum order size that's a bit large:
http://www.favorfavor.com/page/FF/PROD/6705ST_Beach

This compact unit has a pair of 2.5" diameter "optically perfect" acrylic mirrors (5x mirror and 1x) in a compact plastic case.
The case should help protect the acrylic from scratches
http://www.magicfocus.com/orders/MF2011.htm
(? Can a 5x mirror double as a burning glass?)
I've not tried this one myself.