Okay I admit this isn't the greatest fix in fact it's kind of lame, but it does make the cup holder a little stronger. I'm not going to go into to much detail other than saying that the pictures explain it all.
Basically, the little arms on the cup holder are prone to snap off. So, make some supports.
Remove the cover shown in the bottom picture. Do not use it because it won't work with the braces installed.
Make a brace out of some thin aluminum. If you don't have a sheet metal press use a straight edge to bend the bracing clips into the desired shape.
One thousand and 2 uses for sticky tape.
Peel and stick.
Okay I'm too lazy to take pictures of what it looks like so I'll describe it. It looks like a set of cup holders. Okay, with a slightly visible gleam of silver. A black marker or paint will fix that.