My rooftop aerial ceased working reliably because of a problem with the coax socket in the wall. (Just like your situation, a bit of jiggling could sometimes get it working properly). A simple bit of work with a screwdriver and a soldering iron might well fix it. (If you need to get a professional in, it's an aerial fitter that you need).
However the problem could also be inside the coax plug on the end of the lead that feeds to your TV. It won't break the bank to try another one:
https://www.screwfix.com/p/philex-coaxial-cable-1m/41720