As long as the silicone button mat isn't torn or split and the contacts on the PCB are in good condition, I've usually had good results from simply cleaning the contacts.
My usual procedure is first to clean the PCB with a low residue contact cleaner. Its advisable to be very cautious if it has carbon contacts on the PCB as some solvents will soften the carbon ink and make it far too easy to accidentally wipe off, so test whatever you use with a fresh Q tip lightly moistened with the solvent gently on one carbon track, (preferably where its used as a bridge that could be replaced with a soldered fine magnet wire jumper rather than an actual contact pad) to see if any carbon transfers to the Q tip. I also examine the board for obvious defects like cracked solder joints and repair any I see at this stage.
Next I wash the mat with hot water + a little dish detergent to remove gross oily contamination from handling and plasticiser migration, rinse it thoroughly, then dry it. Depending on condition I may also wash the plastic upper shell. If the remote is in particularly clean condition, with no signs of contamination, I may skip the whole washing step.
To clean the carbon loaded contact pads, I use cartridge paper (or heavy copier paper). Put the paper on a flat hard surface, and push each button in turn down so its contact pad is flat on the paper while pulling the whole mat sideways for an inch or two. You are doing it right when the contact pad leaves a dark streak on the paper.
After all the contact pads on the mat have all been cleaned once, partially reassemble the remote enough to test it, and note if any buttons are making poor contact to investigate further. Check the board contacts with a known good button pad pressed down at the faulty position to see if the bad button is due to a bad pad or a problem with the board e.g. a loss of contact at a via or cracked carbon at the edge of the copper track. Printed carbon contact board faults are often fixable by lightly abrading the track and contact then bridging the break with silver conductive ink, which *MUST* be allowed to fully cure.
If its the contact pad that's at fault, inspect it for damage and if none is visible, clean it again on the paper, pressing harder and pulling it further to expose a fresh surface layer with hopefully restored conductivity. Gluing on any sort of replacement contact is a last resort due to the difficulty of getting good adhesion to the silicone mat.