Hi,
Long time ago i had a big problem with one of these elastomeric connectors too. It was for a digital volt meter that i liked but the display was missing some segments (LCD). When i looked into it, i found the connector was not making good enough contact with the glass on the LCD. When i pressed slightly it worked, but when i released it it did not work again.
The fix was to install a small black binder clip, which kept pressure on the connector at all times. After installing, the silver metal 'handles' of the binder clip are removed, and what is left is just the black spring part of the binder clip. That lasted for many years, but eventually the whole meter started acting up so i junked it. I got another 10 years or more out of it after the fix however.