I have never had a problem taking vacation time or sick days. As for planned time away, I make sure my clients know well in advance that I’ll be away and we plan their homework or workouts while I am away. If I go away for an extended period, like last year when I took 6 weeks off in a row to travel back to the states (we’re active duty military serving in Okinawa, Japan right now), I’ll give my clients workouts they can do on their own while I’m away and then I try to contact them once a week via email to stay in touch and see how things are going. After all, I choose to take the time off, they did not!
As for sick days, my clients tend to be very understanding and know that these things occasionally happen, to me or my kiddos. I don’t make a habit of it and I always try to reschedule them for later in the same week. If not, they get a credit toward their next month’s sessions.