If the skin is intact, take a close look at it.
First, look at the sides of the dou, where the edges of the skin are glued down. How does it look? Often, the edges of the skin will start to peel up, separating from the dou. This itself isn’t a problem. As long as the skin on the topside of the dou is fully glued down, tension will be fine. If this is the case, you can put some elmers glue on the peeling skin and reattach it.
Now, press topside of the dou, where the skin is glued to the wood. If it looks and feels firmly flat, then it is fully glued down. However, if the skin seems slightly raised and depresses when you push down, that means the glue has disintegrated there, and the tension has dropped. The skin should either be replaced, or the price significantly lowered.