sticky situation

We have bi-monthly meetings for our Germany program on Wednesday nights. The professor leading the trip strongly recommends that you attend, especially on administration nights (all the paperwork must be turned in, etc.). Well I missed the last meeting because I was sick for three days, but I didn't feel too bad about it because it was just about the history of Germany. The meeting would have been informative, but if there is something that I'm dying to know, I can look it up. Well this next meeting is the biggest meeting of them all, so it's obviously the most practical day for my new boss to schedule my training. I would have requested off, but my employer has already had to reschedule things at my expense, so I wasn't about to pose another problem. But now I have an issue with my professor. I will be applying to dental hygiene school for next fall, and I need a letter of recommendation; he's my letter of recommendation. Now I wouldn't be too worried about this situation if he hadn't stressed a million times how crucial this meeting is. Hopefully he will be understanding of my predicament, but I think I just bit the hand that feeds me.