it doesn't remember the computer that you are trusting, it is asking you when you plug into a computer if it should trust that computer (allow it to access the data on your phone) or not trust the computer.
That's not how it's supposed to work.
When you press "Trust", it should remember your approval for that computer.
At a minimum the computer needs to have a recent version of iTunes installed, and some people have reported that they can only get it to stick if they sync their iPhone with iTunes on that specific computer after trusting it.
really annoying. happens to me every time i plug into my usb in my mercedes c250