Depends how much you want it I suppose. I've only ever had situations that are vaguely similar. I have found it better to stick with the price but instead offer periodic free cleans while doing the more frequent cleaning. That way, your price rather than the discounted price is ingrained into their minds and there is less likely to be hassle when you start cleaning at the more normal, ongoing, correctly priced frequency. i.e. when you start the less frequent cleaning, if you've been charging your correct rate, it won't look like an increase. Maybe every 6th clean fre, for example (you may have a different number in mind). The other upside to this is that if you skimp a bit when cleaning so frequently, it probably won't be noticed. You could probably get away with doing one sixth less work making the discount nonsensical anyway.
You just have to know how to play these people at their own games while letting them believe that they've won.