At first I thought I'd need to buy a new SP, but then I realised the problem could very well be some filth having built up which I could perhaps remove.
It can be dirt build up under the button, but overtime, the surface of the contact under the button can get a layer of (not sure what it is, really) oxydation, I guess, that need to be rubbed off. That could be the problem. Although you need a tri-head screwdriver to open the case and access the insides. If you do so, remember to clean the whole console, to prevent other buttons from acting up!
Always wash your grubby little hands before touching your machines.
And no dipping your chips or licking your fingers while playing. Or I'll put them in a vice... along with your GBA.