Point 1:
Even though the signal strength at the transmitter normally remains constant, the strength of the signal received by your aerial can vary quite a lot. It's affected by the length of daylight (which determines the height of the reflective layer of the earth's ionosphere), the weather (which can affect the transmission path), the 11-year sunspot cycle and individual solar flares on the sun's surface.
Point 2:
In a perfect world the lengths of the elements on a TV aerial should be exactly matched to the incoming frequency. Since every channel is on a different frequency you theoretically need a different aerial for every channel you watch. Clearly that's not practical, so we use aerials which are a 'rough match' to all of the incoming frequencies. Consequently each aerial will be better at receiving some channels than others.
Point 3:
Different models of TV sets have different 'sensitivities'. (i.e. their ability to 'pull in' weak signals).
Putting it all together:
Your aerial is weakest at receiving the BBC group of channels. When the received signal strength drops (due to the conditions mentioned above) it's 'borderline' as to whether a particular TV set can resolve them. Your bedroom TV has got good sensitivity, and can cope with the borderline signal. Your other TV has got poorer sensitivity and can't.
Solution:
Since the signal is strong enough most of the time, a simple signal booster might well do the trick. Otherwise you need to replace the aerial (and, just as importantly, its associated cabling).
Chris