It is likely the same problem as most sticky buttons. Pressing hard and with proper alignment then cuts through whatever dirt or oxidation is preventing proper connection (I assume this is not a sticky drink spilled on it and left there).
I can't necessarily give a timeline for it getting worse but it will and would not be surprised to hear it happens in 2 weeks either, though could be years before it makes things truly unplayable.
You can try cleaning both the board (electrical contact cleaner should do if you have some, don't use automotive) and the contact bits on the rubber pad (no real suggestions, I usually go mechanical, some try adding bits above the pad/between the button and pad to decrease effective travel distance, and be wary if you are using chemicals in case one happens to be solvent) but replacement of the pad is pretty much the ultimate goal for a fix. I don't know if there will be many nice third party replacements, and while there probably will be someone that cannibailised a 3ds and selling it on for parts (at some kind of markup mind you) on the usual suspects then you also have the same thing to face (replacing bad with not yet bad but on the way as it were, though that might still be measured in years).