As someone who's been there and done that, I can attest, once and forget it. I know how much you want to apologize over and over, but unless she has an illness that may make her forget, like a bipolar mania episode etc, medicine w/e... SHUT UP lol.
I apologized over and over and got her so pissed off and sick of it, this is probably a main reason she doesn't approach me much anymore. Now, I haven't been here much and I can't remember if / what you may have done, or how serious it was, but I was only apologizing for small things (I didn't do any REAL mistakes) like, not being affectionate enough, not listening well and anger issues.
So yeah, I'd agree, back off and start building the trust.
Think of it this way, and you may already know, but, every time you guys have a chit chat about ANYTHING and it doesn't get awkward, you're building trust, even in that small moment. Why? Because later, she'll think "Wow, we've talked a few times and haven't griped or talked about 'things' or made me upset" or similar, ya know?
It was hard for me to grasp this concept, but it's real. So like you stated, start building that trust!
Time heals all, btw. Remember that. She may say NOW that she can "never" get past things, but time does wonders. Build trust, give it time.
I'm no pro, take what I said just as what I've experience.
M: 36/W: 28 T 11yrs / M 7yrs /1x 3yo D Sept: W Cheated w/ teen, BDrop. W Beast. Hated me. Oct: 18 (M license)W Asked for D Oct: 31 (Anniverary)W Paid Lawyer Nov1st: Both moved.