Clueless And In A Fog wrote:
...To make a long story short ....

If the plug that powers the downstairs TV and converter is pulled from
the wall socket, the TV upstairs works sporadically.

Many people have theorized that there may be a problem with the house
wiring, but is the splitter and/or converter an active electronic
component that requires power? That could 'splain why the upstairs TV
doesn't get a good signal when the downstairs components don't have power.