Could be the signal strength, is the antenna a leftover from when you had analogue service? If yes then it might not cover all of the digital band..
Also could be simply that you're on the outskirts of the signal area, some mux's will work others won't.. Also could be that the BBC one is on low power for some reason..
There is a website out there which can help determined if it's a signal problem, try
http://www.wolfbane.com/cgi-bin/tvd.exe? and it should tell you the direction and type of antenna needed for reception on ONE tv, more will reduce the signal
Where I am an antenna upgrade worked fine for a few years but when we tried splitting off the antenna we lost some if not all the channels, a simple masthead amp (ebay for less than £20) cured it all and now runs 4 tv's off one antenna