The root problem is that the springs used under each contact are a bit too strong and the weight of the remote isn't enough to overcome all 3 springs consistently. This leaves one contact not making good contact. Cleaning can only help so far. It can't overcome a flawed design.
If anyone doubts that the springs are the culprit, try this. Put the remote down in the cradle. now, gently press on one side near the contacts. Does it tilt easily? Now try it on the other side. Now, press in the center of the screen. Did it press down slightly?
What's happening is that the springs are actually holding the remote up. When that happens and you have 3 contact points, unless the 3 points are in a perfect line, one of those 3 contacts isn't going to make a good connection, if it even connects at all.
Logitech either needed to use slightly weaker springs to allow all 3 contacts to be made consistently, should have placed the contacts at the same end as the battery (slightly heavier), or used a capture mechanism to ensure good contacts on all 3 points.
Besides monthly cleaning with CAIG's DeOxIt and ProGold, I simply put a tube of Daisy BB's on top of the screen. This always works.