RE: when to stop trying
I think a lot of people are overlooking why someone would be breaking props and generally crashing. As stated before, its either the instructor isn't teaching very well or the student isn't listening or is freezing when the plane is a couple of feet off the deck. I am an instructor in my club and from what I've read, I know exactly what is being done wrong.
For starters, the breaking of props is because you are coming down on the nose which means you aren't flaring or you are running out of elevator and cannot flare anymore causing you to sink too fast. Anytime I see a trike plane bouncing on its landings its usually because they are coming down on the nose gear as opposed to touching the mains first.
When you are coming in for a landing, your nose should always be positive (not by much). You control your decent with the throttle. While keeping the nose positive, you should start moving into a good glide decent. If you are sinking too fast, just burp the throttle for a second or two and then resume your landing approach. Most people just bring their throttle down to idle and coast in. While this can work, it doesn't always look like a perfect landing.
Generally, your instructor should know when he/she needs to take control of the plane and prevent a crash. Of course, when it comes time to make that final landing, you just have to trust yourself and relax. Too many times have my students crash on their landing because they just freeze up and decide to let it land no matter what. You cannot always save a plane from a student when they are 2 feet off the deck.
When it comes to my students, I make them do semi-slow speed passes down the runway. This is a prelude to teaching them how to use the rudder to control their direction and to feel comfortable with the plane moving so slow since the controls are a little more sluggish. Each pass is done lower and lower until they are about 10 feet off the deck. If they can fly straight down the runway and a 1/4 throttle and aren't making any mistakes, only then are they allowed to make a landing attempt.
My advice is to try a different instructor. I remember the guy who trained me. He would break at least 4 props every flying day and he was supposed to be the instructor. It wasn't until I soloed and learned the proper way to fly before I could instruct others. There are a lot of people with a big heart who will give up their time to train, but doesn't always mean they should be training.