I just had a shim fall out of the scabbard for my cia/hanwei albrecht longsword. I've had it for a few years and never suspected it. Based on the fit against the blade, it was seated further down in there, not up by the throat, and I have no clue how to go about repairing the problem. The scabbard barely has any hold on the blade anymore. Am I a thte point where this is just a valid excuse to get a custom scabbard instead?

I would suggest gluing a piece of leather or paper or thin cardboard up by the throat, where you can access it or remove it if it becomes too tight. Trying to install a wedge deeper is just going to cause frustration.
Note that you might need a thinner piece than what fell out. Because I believe that particular scabbard is wood cored, a piece of card stock and wood glue might be all the investment that you need.
I'd suggest taking a rectangular piece of card-stock about 2" long and a bit narrower than the mouth opening. Put a 90 degree bend in it and insert it into the mouth with the bent piece hanging out over the shoulder of the mouth and folded down the outside, where you can hold it. And try to insert the sword. See if it's thick enough to give the resistance you want. And yet not so thick that it makes the sword wedged in there tight. Do this with several thickness until you find the right one/ones. You might have to glue paper together to get the right thickness.
When you get the right thickness, apply glue to the side that contacts the scabbard and insert the sword to let it dry overnight (Pull the sword out a couple of times before leaving it to dry, to make sure you didn't get any glue on it....otherwise you might damage the finish or glue your sword in place.)

Hanwei scabbards aren't horrible, but in my opinion they aren't worth investing any money into. Trying to disassemble it and recover/assemble it, would be more work than just making a new one yourself. Obviously if you have the money and patience, get in one of the manufacturer's queues like Tod or CSS or Triton et.al. Or you could invest in some materials and venture making one yourself.

I have the Albrecht II sword as well, and though it didn't cost much, I feel like it deserves a better scabbard than what it came with. In the mean time the stock scabbard is good for transporting it and protecting the finish.

A small piece of leather lace cut, wedged and crazy glued into the corners of the opening of the scabbard has worked for me in the past and can be replaced easily if it gets loose or falls out eventually..

It takes only a very small piece and you have to be carful to not make it too big as forcing the sword in might damage the wooden core of a scabbard if the fix ends up being too thick: You might have to shave down the leather lace pieces until they give just enough tightness to hold the sword in the scabbard if held upside down but release the sword if it's given a light shake.

Oh, be carful if testing for this to not grab at the edges of the sword when it does fall out: Grabbing for a sliding sword out of a scabbard is a good way to loose finger tips or cut into tendons. ;) :D

The above-mentioned methods will work, however, I advise going the custom scabbard route. :D