Rabbit syphilis can take quite a long time to cure. What has happened in you bun’s case is more or less certainly that his first round of antibiotics (pen g shots) wasn’t enough.
I think your vet could prescribe more meds to you if you call them and tell them that your bun’s symptoms have returned. This is very common with rabbit syphilis so it shouldn’t come as a surprise to your vet. It would be really great if you could give Thumpers his shots so you don’t have to take him in for every shot.

He probably didn’t become reinfected. The treatment probably just wasn’t long enough. The series he received probably knocked a bunch of the bacteria out, so you saw symptom improvement. But if it wasn’t all eradicated, then they will start multiplying again after treatment ceases. Then symptoms begin to reappear.

I don’t recommend purchasing penicillin over-the-counter. Penicillin meant for livestock varies widely in strength (it isn’t consistently formulated). It’s better to get a prescription from the vet so you can ensure your bunny is getting the correct dosage. You may be able to ask the vet if you can administer the shots at home. I know some people have done this, but you have to be comfortable with doing it.