You may have left rubber fragments behind. Metholated Spirits or CO cleaner- something that doesn't remain and will remove any oils or other foreign matter. I have fixed hundreds of IR remote controls, which use a silicon rubber membrane with all of the buttons moulded into it, and one of the things that happens with them is that a film of oil appears across the surface of the contacts and prevents their touching. I normally wash it all in Palmolive dishwashing liquid (diluted muchly with water) and then rinse with clean water, dry in the sun. If that rubber strip is reversible, you could try end-for-ending it. The dishwashing liquid is safer, if you use anything more potent, don't leave it there for long!
Another thing that happens with the remote controls is: The buttons have a coat of carbon paint. Continual use deposits carbon across the contacts on the PC board where the button touches. If your rubber strip uses carbon for the conductors, you might have that problem. I've fixed several of the missing segment problems but never even considered that possibility.