If the Allen key is turning but not grabbing and you think that your socket is rounded or stripped, maybe it is not. Maybe you are using a metric Allen key, instead of an imperial one (or vice versa).
As you know, Allen keys (like many other tools) come in sets. I grabbed the set that came with my tool set, found the largest key that can fit in the socket and tried turning. It was turning but not grabbing. I thought that the socket was rounded. Later on, I realized that there is another set of Allen keys in my tool set. Again, I found the largest key that can fit in the socket and tried turning. This time it worked like a charm.
Turns out, the first key that I tried was from a metric set, where the key was 3 millimetres. The second key that I tried was from an imperial set, which was 1/8 inches (which is 3.175 millimetres). As you can observe, these are "almost" the same size, but being "almost" the same size is not enough. That additional 0.175 mm that is brought by the 1/8 inch Allen key was what was necessary for the key to properly fit the socket.