I was caught off guard by this situation during my first game too, since the game mechanic is implied. I arrived at the same conclusion Toqtamish described from a different angle:
The situation is that an Ambush Asset is essentially a "1-shot" type of card. Once the runner exposes it (or accesses it but does not trash it), the card does not automatically discarded, but remains in place in its original state.
This implies that it is up to the Corp player to trash the stale Ambush card to replace it with a new card that will be useful again. Otherwise the Hacker will likely ignore that server for the remainder of the game, which could be fine for the Corp player too, if he is not interested in using that server any further.