Try pressing firmly on trackball and scrolling in direction it does not work.
Sounds like dust got into it.
If that doesn't work try popping the trackball out comes out easily pull the silver ring out then flip over bb trackball should come out inspect for dirt and grime clean accordingly
Thanks! I tried removing the trackball (found directions on this site!), I was worried I would total my Curve but it was much easier than I thought and....it worked!!
It happened to me several weeks ago, try pushing the trackball and rolling, pressed, toward it does not work, do it several times until you feel it is working again, also you can clean with cotton and alcohol, do it without the battery.
Mine stopped working and cleaning with alcohol and dust remover did nothing. It just went BAD so I went to Verizon and they replaced it for me for free. However, I did buy two spares online so that it can save me a trip in the future. Be careful with the silver ring though. I was too aggressive the first time and snapped off the tabs.