Yes, they can fail too. See: http://www.vintage-radio.net/forum/show ... hp?t=59610
To my knowledge, besides self-healing events, internal corona discharge (which progressively eats away at the metallisation) is what eventually does them in. Of course, the only consequence of their failure in EMI filters is an increase in differential-mode interference, making their failure even more covert than typical age-related failures (dried-out electrolytics, etc.). It could be that you have a PSU (maybe several) with an X capacitor that has been practically open circuit for years, without knowing it.
Not having a capacitance meter of my own (yet) I can't personally attest to that experience, but it's something to take notice of. Could we knock points off units with low-quality X caps? There are endurance tests for X and Y caps, but it's not as though the makers of crappy 'lytics don't give endurance spec's.