The collet is supposed to have a portion that as you "screw" the collet down, the interior closes in on the shank. Look at the grooves cut through the collet in this picture. You can see that it is designed to close in on the shaft. If that part is missing or broken, it won't hold the bit.
If you've tried other collets and other bits and it doesn't hold, then you probably have some defect in the threads, either cross threaded or possibly the threads are damaged so the collet nut still rotatess, but only turns in a circle without going further down the threads. You can look at the threads with a magnifier to see if there is something about the thread that doesn't look right. Or take it to a tool service station and have them look it over.
Stick's suggestion about lubrication or too small a shaft. 12mm vs 1/2 inch can be enough to prevent holding tight. The collet itself really doesn't change size much, it is, after all, a pretty high quality of steel, and very carefully machined. But they do break or stop working right, for example, the Bosch Colt is known to "eat" collets. We're talking a few thousandths size changebetween loose and tight.
You didn't say whether the problem persisted with other collets and bits you know to have worked in the past. If no collets or bits tighten, I'd bet on damaged threads on the shaft.
The more I do, the less I accomplish.