When discussing these types of things, terminology is important. Most hotels are franchises (meaning they are locally-owned) that are NOT managed by Hilton. Of the 5,500 Hilton branded properties, only about 285 are managed by Hilton.

The list of properties using Hilton Management Services can be found on their website.
Hilton Management Services | Portfolio of Properties

So, chances are strong that the hotel in question is locally-owned and locally-managed. That fact doesn't really change the answers to questions, but it does matter in terms of who is responsible for fixing errors.

While I worked in multiple hotels, I never worked at a Hilton hotel, so my knowledge is based on talking to colleagues. But, every hotel group requires franchises to use the same property management system (PMS). In some cases, more than one PMS is available. For example, full-service hotels will have one PMS and limited/select-service hotels will have one with fewer features.

I think Hilton's PMS is OnQ. (Don't quote me on that, though.) That would be the US-based PMS. Since the hotel in question is outside the US, it might be different.

Certainly, hotel IT isn't rocket science. That said, it can get complicated when you consider all the different sub-systems that must communicate: Reservations, Front Desk, Key Systems, Life-Safety Systems, Telephones, Entertainment (pay-per-view), Housekeeping, Restaurants, Sales, Catering, and Accounting. In some cases, the PMS must support sub-systems provided by multiple vendors with multiple formats in multiple languages.

I can't directly comment on Hilton's requirements. But, the process of updating Hilton Honors would either be automated or batch on a schedule. One of my hotel jobs was Income Auditor in Accounting. In that role, I audited the night audit. Once I reconciled everything and entered it into the ledger, the system would forward the appropriate information to Central Reservations where frequent guest points were added to guest accounts. So, our points got awarded the following day, except on weekends. Stays for Fridays, Saturdays, or Sundays were awarded on Monday.

The financial benefit would be not having to pay for those points. There's no IT cost savings because the franchisee would be required to use Hilton's PMS.

Given what you've described, my best guess is that it's a bit of incompetence. At some point, some employee is doing something incorrectly (or skipping a step). Because this hotel is "out-of-the-way" and potentially has fewer guests who collect points, the management may not even realize this is a systemic problem.

The best way to get a problem fixed is to talk to someone with the power to make changes. Honestly, no one you can reach by phone or email at Hilton Honors is going have that power. You're only hope would be for an Honors representative will send your complaint up the ladder. But, you'd need that request to go up multiple rungs on that ladder.

Unfortunately, it's going to be a difficult task finding the person responsible. Where I worked, that would have been the Regional Operations Manager or Regional Revenue Manager. Those were people who oversaw hotels and ensured that the rules of franchise agreements were upheld.

My advice would be to contact Hilton Corporate. I'd try writing or calling one of the offices listed under the "Corporate, Non-Media Contacts" section. Be succinct and mention that you think there's a systemic issue with how a franchise is handling Honors points.

https://www.hilton.com/en/corporate/contact-us/

I completely understand why this is a frustrating issue. There's no reason why guests should have to repeatedly ask for points to be awarded as promised. That said, trying to fix these problems isn't your job. It might not be worth the time and energy. I'd be tempted to just create a spreadsheet and spend 1-2 minutes submitting a point request after every stay via the Honor website.

Good luck.