Answer: (C)
In context, we learn that players with extant recordings (work still in existence) seem to ‘weather’ time better than those who do not have extant recordings.
(C), which means to hold up/endure, works best.
(B) means to barely survive, a meaning that does not quite fit the context.
(E) has a few meanings. One meaning is something like "suffer through," which makes this tempting. We sustain blows, injuries, or other painful things. It doesn't mean we survive them, we just get them. In this sentence, we need something that means suffer through, but not be defeated by--and that's "withstand."
Besides that, we can get a sense that "sustain time" doesn't work just by ear; it's not a normal English collocation. "Withstand time" is much more natural.