I have an issue on my eeepc where certain keys: the grave accent/tilde, tab, and caps-lock on the left, and the right-side fn key and sometimes arrows on the right, stop working seemingly at random. Shifting the keyboard slightly left (by prying from the right) makes the right-side keys work again, and shifting it slightly right (by prying from the left) makes the left-side keys work again, but it's very difficult to balance it so that both sides work. If I pull the keyboard out and hold it up, all keys work fine. My first theory was that the keyboard was somehow shorting at one side or the other, but adding insulation behind the keyboard did not seem to help. I feel like I would have a better chance of fixing the problem if I understood the cause; any idea what might be going on?
I don't know about Eee PCs, but most keyboards are connected with a very thin, wide, ribbon connector which just slides in and out of a socket. I'd guess this is loose, and so wiggling the keyboard helps establish the connection again.
If so, you might want to open it and try to push the ribbon connector into the socket more tightly. Depending on your level of comfort in taking small, tightly packed computers apart, of course.
If you DO want to do it, try searching for a maintenance guide for the Eee PC online. Actually, that will tell you what kind of keyboard connection is there, without having to open it up first.