I think the TV license fee is for Operating a set Capable of Receiving - you don't have to be watching it - it does not need to be tuned into any signal. You will not get a refund.
The two channels that disappear - they go away because of a weak signal - quite likely the signal is still there but too much of it is being lost for the electronics to properly decipher it - with an old analogue signal you would see a very fuzzy image with interference - not so with a digital tuner - it gets to a point where it just packs up.
Weak signal - fact of life - try your best not to let it get you down. Try Radio 4 - it has better pictures.
https://www.youtube.com/watch?v=YS5mVoqJpUk
Peccavi
April 2013