Yes, they can and do wear out, and are relatively easy to replace if you're handy.
GFCI's sense a disparity in the current flowing OUT through the hot (black wire) and current coming back through the neutral (white wire). If it senses more current going out than coming back, it trips. This is based on the presumption that some of the current is flowing back through an unapproved ground (like a human body
)
Faulty wiring, nicked conductors, and moisture can also cause a GFCI outlet to trip. I've also seen them trip from large inductive loads (motors) starting and stopping.
If you replace it and it continues to trip with no load on the GFCI or downstream outlets, then you probably have a faulty wiring issue.