Oh no...I feel so bad for you

please don't be hard on yourself, absolutely not your fault *hug*
The CSR made it sound clear that this is different from just purchase limits which reset after a time period. H and LV are the brands I deal with the most and I know both have limits, from number of pieces you can buy to the number of different stores you can buy from within a time period...but none of those should restrict you for life, which moves into "banning the customer" category. Yes, they also do ban people for life (with an official ban letter and all), common reasons are reselling, massive and unreasonable amount of returns, very bad behavior in store...etc but none of which should apply to you.
I agree with others that the most likely reason was the reseller one. Maybe whatever algorithm they use to flag resellers wrongly flagged you. H does take action to ban resellers from time to time, although obviously they don't catch them all or even care to sometimes (I know my home store has some resellers too).
But assuming that's the case, it is kinda stupid that they are only banning bag purchases (instead of everything), and only on H.com but not in stores. If it's truly a reseller, don't you want to ban them everywhere? I do think there is a slim chance that the CSR was mistaken (but I also wouldn't be surprised if companies just have really stupid rules). By the way that CSR definitely sounded like a HORRIBLE person. So sorry that you had to deal with them.
Also I don't know if I believe in the "nobody can help you" part...maybe the CSR doesn't know anyone can update your account in the system or maybe it's not in their rulebook, but if someone with enough authority orders so, the IT people for sure can, I dunno, edit it in the database. This feels more like a rulebook problem than a technical problem, and rulebook problem often means finding the person with enough power to override the rules...I don't know who that would be though & and I doubt it's your store's management chain (I get the feeling that H.com operates very independently). I hope more veteran members in this forum have better suggestions. But then again, I completely understand if you don't even feel like doing that, given the amount of trouble and headache they've caused you. I'm so sorry your H experience has been so rocky