If one applies for/granted Aid & Attendance funds at one level, can/will it be increased if the beneficiary's finances drop further?

If the VA doesn't get the question, we are sure unlikely to do so.
I know I haven't a clue what you mean, myself, so can only wish you good luck.

Are you talking about if one spouse dies? The way I understand it is a married couple will get an amount for both of them. If one spouse dies, the other will get the amount for a now single person based on what income they now bring in.

Here is a chart for 2024

https://americanveteransaid.com/newblog/va-aid-attendance-benefit-rates-for-2024/

A person has to qualify for Aid and Attendance funds from the VA to begin with, by having under a certain amount of $$$ in the bank. The amount of the benefit is a fixed sum that does not change regardless of needs. The person has to be in Assisted Living or have in home care due to needing help with several ADLs, substantiated by a doctor in writing. The amount of the benefit adjusts annually due to cost of living raises, minimally, and that's it.

Once the veteran dies, the spouse applies for benefits which are automatically at the maximum amount available, IF they qualify by needing help with ADLs. It's a fixed and permanent amount that does not change according to needs.

If 2 spouses are alive, they receive the couple's benefit. In 2015 it was $2400 for my parents in Colo. When dad died, mom got $1400 for the remainder of her life until she died in 2022, even though her costs went up in Memory Care Assisted Living.