BBC Four HD, BBC News HD and Quest HD are all on the often-problematic COM 7 mux which can usually be picked up at UHF channel 55 when tuning. This mux is outside of the ideal range of certain types of aerial, is often broadcast at a lower power than the others and is also susceptible to interference in certain types of weather. Some of the UK's transmitters don't broadcast it at all.
You could start by checking the signal strength you get for a non-problematic channels (try BBC One) and compare it with BBC Four HD. Do this by selecting the relevant channel and then go to 'Signal Condition' in the Freeview tuning menu and make a note of the signal quality and strength. My guess would be the BBC 4 HD values will be a lot lower, which will explain the issue.
Channels returning to their original positions after retuning is normal behaviour, BTW.