95 Voyager AC Damper door wont stay cloed.

Welcome to Allpar. The low vacuum on acceleration may be from a leaky 'one-way' vacuum check valve that comes off of the brake booster hose junction or intake manifold. This may allow vacuum to drop instead of holding the doors in the selected position.
It should be shown on your underhood vacuum map label as an in-line 'film canister' sized or disc-shaped' valve. The valves are usually available generically at auto parts stores in the Help section . You should only be able to blow through it in one direction and not the other. I would replace this first if it is failed and see if leaks remain.

I found the check valve on the brake booster thanks to your accurate description. It holds in one direction only. Thanls for the info. Its got to be losing vacum farther down the line. Thanks so much for the info.

Look for a split or jabbed plastic line or rubber end or torn actuator diaphram. A service manual may help with line colors and routing.
The HVAC control itself may be the source of the leak. A good used one my be around. These were fairly corporate across many models in their application.