Hi!
No need to apologise at all!
I am really sorry to hear this - that's such a frustrating situation, especially when it is out of your control.
It is highly unlikely that they would hold this against you next year, particularly if you have been transparent about the situation. If there is genuinely only one AC date, that is a logistical issue that is out of your control.
If you do withdraw, I would thank them for the opportunity, briefly explain the unavoidable work commitment, and reiterate your interest in the firm and reapplying. The graduate recruitment team understand that people have other commitments alongside the process, so they'll be understanding!
Getting to the AC stage shows that you are a strong candidate - I'm sure you'll have plenty more success moving forward