Is your coach comping you lessons? Is she letting you pay "when you can"? Is she sending bills infrequently, so that you don't have to worry about them? How about giving you "discounts"?
What a great deal. Here's what one coach told me about these practices.
According to this coach, high level coaches will comp, discount, or carry students to pay when they can, so that if they try to switch coaches, Coach Old can go to Coach New and say, y'know, they owe me a lot of money; if you take this student I will report you to the PSA". Taking on a student when there is an outstanding bill to the old coach is strongly discouraged by the Professional Skaters Association and USFS. Basically, by not insisting on full, timely payment, the coach is buying your indenture. As long as you owe money, you can't switch.
Here's the lowdown, in ascending order of bad idea:
Rating: not too bad, if you control it
This is the coach's problem. If they can somehow afford to live without getting regular paychecks, that's their worry. You don't have to play along. Simply write that check every week anyway, and when they finally bill you, you have, in effect already paid it.
Rating: get it in writing
If you are taking a lot of lessons, a couple to several hundred dollars per week, discounts make sense. You are a guaranteed income stream for the coach, you're reducing his administrative time, and you're a valuable customer. But beware of discounts that are too deep. I've heard of coaches reducing fees by as much as 70%, and then coming back when there's trouble in paradise and stating that the family "owes" them, not necessarily money, but loyalty. If you are getting a discount, get a contract that states the discount and exactly what the expectations are (for instance, I would say it's perfectly reasonable for a coach giving a significant discount to expect the student not to switch coaches mid season).
Rating: too good to be true
Again, this can be a way for an unethical coach to buy your loyalty, in effect to indenture you. Now, lots of coaches comp talented kids who legitimately can't afford lessons; I've done it myself. But if you're a well-off family, or have a competitive skater, beware. TANSTAAFL (There ain't no such thing as a free lunch).
Skate now, pay later
"Don't worry, just pay me when you can." Bad idea. Bad Bad Bad Bad Bad idea. If you cannot afford to pay now, you cannot afford to pay. Period. Cut back on lessons, raise money through community fundraisers or letters to friends and business associates, whatever. Do not buy what you cannot afford. That coach will never let you go. If you carry a large balance and want to switch coaches, your competitive career is over. And if you're not a competitive skater, what what what are you doing?