Once you out-trade a villager's specific option, you lose it: it has a large red X on it, and you cannot make that particular trade anymore. Is there any way to recover options that fall to this fate?
Yes, you need to trade with them using one of their other trade options.
From the Minecraft Wiki (emphasis mine):
Villagers will deactivate an offer if the offer has been used some number of times and it is not the villager's only offer. The chance of an offer's deactivation is random, but an offer must be used at least 3 times before it is eligible for deactivation. After an offer has been used 13 times, it is guaranteed to be deactivated if you close the interface after trading it (this is true even if all 13 trades have been done at once). Trading the last offer may activate an offer again.