Yes, I have many 12v halogens lurking around here, and they all eventually succumb to the lamp-connector failure.
I have a bag of replacement connectors, and am working my way through them.
Typically, what you'll find is that if you get the lamp out of the fitting, but dangling on it's connector, then you can carefully wriggle the lamp in-and-out of the connector a few times, and it will go on and off.
Removing the lamp from the connector will show that one pin will look dark and corroded.
The pin on the lamp can be scraped clean, but this is a surefire indication that the connector really needs replaced in this case.
I've recently replaced most of my outdoor 12v halogens with drop-in replacement LED equivalents, and that will (hopefully) mostly eliminate this problem.