Maybe this will help ... My wife was having a continuing "Stuck Slider" problem on her phone. When I removed her screen guard (plastic clear cover accessory), it now works all the time for her. If you have a screen guard, try removing it to see if that will work for you.
I know there is another page about problems answering the incredible. I have a protective screen too. Often, I couldn't get the phone to answer an incoming call. Another forum said when you slide one finger down the middle of the screen, you should slide another along the case. It creates an electrical ground, according to the other site. I am batting 1000 on the first try using this new technique.
My wife had the same problem. We use invisihield and that was not the problem. The problem was she was hovering another finger or two over another area of the phone causing that to register which threw the swipe off causing it to stick. I pointed this Out to her. No problems since.