I agree with everyone else - don't worry about falling off. Falling off and getting back on has taught me some of the best lessons and, weirdly, has made me less afraid of riding. I've only been riding for 1.5 years, but that's just my experience.
Also, if you find that you're nervous about something specific, tell whoever you're taking lessons from. I was terrified a few weeks ago after the horse I ride took off at a full gallop with me on his back, and I didn't say anything for a while because I didn't want my instructor to think I'm a pansy or something. But in the end it got so bad that I didn't want to ride anymore, so I did tell her, and she helped me to get over my fear in literally one lesson; turns out I'd been pulling on his mouth too much and was sending contradicting signals to him.
So, sorry, that was a little off topic...but don't be afraid to talk to your instructor or ask questions, especially if you're feeling uncomfortable about something. And I'm sure you're not a bad rider! The fact that you get on after falling off is already really great, so don't worry, things will get better :)
"In riding a horse, we borrow freedom." Helen Thompson