So you have leak(s). When the engine is running you have sufficient vacuum to exceed the leaks. Leaks can be in the actuators or in the lines/junctions for the lines. Leaks can be in either the "lock" circuit or the "unlock" circuit or both. You need a Mitivac to diagnose the problem. Do _not_ just start replacing things.

I don't know how things are routed on a 108, but on a 123 most of the good stuff is under the carpet on the front passenger side. You take up the carpet and identify the junctions. On a 123 the "lock" circuit is color-coded differently than the "unlock" circuit so what you can do is find a junction and apply vacuum and see if something locks or unlocks. Then see if while applying vacuum the vacuum pressure is holding. If it isn't, then you have a leak down-stream from there. As an example, on a 123 I _think_ that the unlock and lock lines found under the right front passenger carpet control the front and rear right doors, the gas cap, and the trunk. So if you try to either lock or unlock from that position and you aren't holding vacuum you need to move one step further down the line to see which one(s) are leaking. So you move down-stream to the line that just operates the rear door. See if it holds vacuum for lock and unlock. If it does, it's fine. etc.

The fact that it locks everything right after you turn the engine off means very little. See what happens if you turn the engine off and DON'T lock the doors, and come back in an hour and see if you can lock the doors then. If you can't then you have a leak in both the locked and unlocked circuits.

I think there is a tutorial on one of the websites, possibly diesel giant, but I don't know for sure.