I have a similar problem - no teeth. Although in my case the problem is not that false teeth keep falling out, but that I find false teeth too painful to wear.
If I'm trying to book someone for the first time, I always do it by email and I always say that I've got no teeth and I will quite understand if she prefers not to see me. Doing it by email gives the woman time to think about it and spares her the possible embarrassment of having to tell me on the phone that she doesn't want to see me. Telling her in advance means that my toothlessness does not come as a shock or surprise to her when I finally show up on the doorstep. And I can relax and not have to worry about how she will react because I've already told her.
In the five years or so since I became toothless, I've only had two women email me back to say that they couldn't cope with toothlessness and they'd rather not see me. Frankly, I'm surprised it's only been two. And I wasn't in the least offended. If they aren't going to be able to cope, much better to find out beforehand. And if you're going to be offended if someone says "no", what's the point of asking them if they're going to be happy about it in the first place?
Apart from those two, everyone else has replied saying they couldn't care less about it, get your arse and your wallet over here quick smart, etc etc.. For which I'm truly grateful to them all.