Yah. I'd bet on dirt. Grab a QTip, grab some rubbing alcohol, and scrub that contact. Hit the rubber contact too.
If that doesn't work, and the rubber dome is still good, there's a trick that served the Atari 5200 community well for many years with it's iffy circuits that rapidly get bad enough to interfere with the controller logic.
Get some superglue and aluminum foil, tear a piece of foil off that's about hte same size as the carbon dot, and glue it to the dot. Once it dries, put things back together. The foil is more conductive than the carbon dot, and makes for a much more sensitive button.
On the downside, you'll likely lose the PS2's pressure-sensitivity on that button.