So this is a ridiculously simple mod to do. And I figure if your cup holder bugged you, you would have already done something similar.
But here we go anyway. I used my cupholder for the first time yesterday, and was too uncomfortable to go around a corner without placing my hand on the cup. So I went and did this tonight, and now have a cupholder which actually holds onto a cup.
Start your search for something rubberized. I ended up going with weatherstripping. It's cheap (<$6), well sized, and already has adhesive on the back.
Split apart the weatherstripping into the two separate sections. Cut about 3" off of one section. Cut off one of the channels (cutting parallel), and try to maintain the most adhesive possible with your cut. Press the rubber piece against the lip of the cupholder, keeping it flat against the top.
Now moving onto the base. Cut out about a 1" section from the other side of the weatherstripping we split before. Press it against the base of the folding lip, trying to keep it as low as possible with the most adhesive area available.
Push it in and see if the cupholder moves smoothly. If not, adjust it by trimming the lip piece until it does. If you mess up, you have plenty of weatherstripping to fix it with. If all is well, move onto the second cupholder, and repeat.
Now you have a cupholder which actually holds onto a cup, and for very little.