I've never had that happen, but, to my knowledge, it's only when the pollinia get removed that the flower fades rapidly. If it's just the anther cap, you should be ok--the flower should last as long as normal.
I'm keeping a close eye on the flower. Okay, you're right, Louis! The orchid still looks fresh and definitely isn't "fading rapidly". . I guess I got a bit worried.

It's been open for only about four days, but I'll post if the flower wilts or something...