How often do boxers fake a knockdown?

It happens once in a while.

once in a blue moon, it is rare.

There are other tactics to get a breather without earning anpoint against you or risking the ref calling the match

I think it happens more than some care to admit. But it can be legitimate. If you get hit with a particularly hard shot that damages you but not enough to knock you down (say really shakes you or gets your legs a bit wobbly), it makes more sense to go down rather than risk a follow up shot that could knock you out. That's clever fighting.

More often than would be admitted.

Like Wrestling it is all setup for the book makers

Some have but very few its when the money is the only reason they are fighting , i believe Sonny Liston took a dive against Mohammed Ali he was found shot dead in the USA  as a lot of people are with the criminal culture they posess