I find similar behavior if I do not have the caliper centered on the wheel. I loosen the nut on the back, re-center it, and usually it works.
Of course, on ANY brake work, make sure cables and housings are good. When in doubt, just replace them. Those items are cheap, and can create all kinds of symptoms (I pay 71 cents each for cables, and $10 for 50 feet of lined housing (from Niagara).
Also make sure the spring on the back side of the caliper is sliding freely. The bottom of the spring slides against a post on the caliper. I put a dab of triflow on the pin (not sure if it helps or not, but it is just what I do).
I also will occasionally disassemble the caliper, clean and grease pivot points.