First of all, you can't move paintings up and down the wall in live mode at all. I'm not sure if that's what you're doing, but I wanted to throw that out there just in case.
To move a painting in buy mode, you first have to place it (which I'm guessing is already done). Sometimes it works better if you go into buy mode, pick it up and take it off the wall, then put it right back on. When you click on it next, hold the mouse button (if you release it, you'll pick it up again), then move the cursor up or down to get the arrow. Once it's at the spot you want it, let go of the button and it should be placed. You can then move the painting to any wall and it will remain at that height.
Another thing I've been noticing lately is that buy mode has become a little glitchy when the family inventory is open: items removed from there sometimes can't be placed unless you drop them back into the family inventory, and when you pick something up to move it, sometimes it's hard to drop it. In case that's what is happening, it is easily fixed by simply dropping the painting into family inventory, then placing it back on the wall. After it's been replaced, try to move it again.
Edit: I'm too slow it seems lol.