Light fixture with one of the sockets doesn't work, do I replace the fixture or can the socket be repaired

It's often possible to replace sockets, but it really depends on how the fixture is constructed. For example I've replaced the socket on old-fashioned table lamp. but found that for a recessed ceiling can fixture it's more time and cost effective to replace the entire can than to try to replace just the socket. And depending on how the fixture is designed it may be difficult to find a replacement socket that is a direct replacement for the faulty one.

Sockets can be repaired or replaced but they rarely go bad. I'd check the wiring going to the socket first.