(1) This is a guess only - as many people report this problem on the internet increases the possibility.

There may be a power supply filter capacitor that has 'dried out' with age.
One possible solution is to try adding a capacitor across the battery terminals to see what happens. Having a small amount of electronic experience would help. As large a capacitance as is readily available. 1000 uF should be good. 100 uF and up will do no harm. I won't give a detailed how-to as this is reallyt only suitable for who this is enough.

(2) Desperation - may even work. A slightly dear solution, alas. Use "Lithium" AA non rechargeable batteries. These are not cheap. The reason that they MAY work is that they maintain a much flatter voltage across their discharge lifetime, and do not droop under moderate loads for much of their lifetime. 2 x AA Alkaline = 1.65 x 2 when new = 3.3V. This is only at the very start.

(3) Expert only: Use a LiFePO4 (NOT LiIon) battery plus a dummy battery.
A LiFePO4 cell gives up to 3.6V and typically 3.3V down to 3V when operating. SO a single LiFePO4 AA cell will give slightly more voltage and less droop than AA Alkaline batteries.

DO NOT use two LiFePO4 cells in place of 2 x AA Alkaline !!! Use a dummy 0V "cell"

This SHOULD NOT cause damage to the camera, but take due care.

(4) Some people report success after cleaning the battery contacts. Seems unlikely but worth a try.