CzarCW:
I switched the spot where by ground wire was connected (along the same ground rail on the breadboard), and it seems to have fixed the problem.
I had the same instability problem, and my 5V wire was connected side-by-side with my ground wire on the breadboard (both at the first pin on top, but on different vertical rails, of course).
Following your advice, I moved the GND connection further down (to the second pin from the top) and the problem is now gone, though for the life of me I cannot figure out how or why.
Thanks!