For example, if you see a lady that is $500/hr and requires a deposit of 20% does that sometimes result in you booking a shorter appointment than you would absent the deposit requirement?  Perhaps you only book 1 hr. because you will risk losing $100 but you would have booked 2-3 hrs. w/o the requirement?

The deposit is a trivial amount of money so I don't really sweat it to begin with. Doing the proper research beforehand greatly limits the risk as well, so I don't tie in the length of the session with the deposit risk, but of course many others probably do think differently. Good question!

It doesn't matter the amount of the deposit.
If she requires a deposit, I move on to someone else.

are the only circumstance that justifies a deposit, IIMO.  If I am booking an overnight or weekend, it means that she is turning down other opportunities to work to keep the block of time open for me, and if I flake, it's a huge loss for her because she's never going to get a chance to see that time to someone else.   This is the only time I would agree to a deposit.  I would never pay a deposit for a session of one or two hours.

Deposits are a hard pass under all circumstances.  Just not worth the risk (money, paper trail, effort ...)

That actually makes a lot of sense. I never require deposits but it does suck when a gentleman wants a 4+ hour date and then has to cancel but I believe in flexibility so *shrug* I think I also get more date requests because I don't require deposits so maybe it evens out.  

Requiring a deposit means I won’t be seeing her at all

I doubt that providers who serve deposit paying mongers find that it impacts the number of longer term dates they book.

But I repeat myself.