My sealed system has been losing pressure very rapidly, and I've finally
found out why. When it heats up, the pressure on the gauge rises
dramatically (3bar!) and water is ejected through the pressure relief
valve. All is then well until the heating goes off, at which time the
pressure drops right down to zero.

I'm assuming that there must be air in the system to make this happen
(after all, water doesn't expand that much), but where is it? All the
radiators are hot top and bottom, and none of them will bleed any air. The
system runs quietly, with no bubbly sounds. Can it be that the big red
pressure reservoir thing above the boiler (forgive my technical language)
is full of air? It's at the highest point of the system, more or less, so
that's where the air should end up. If so, why does water get vented when
the pressure relief vave opens, and not air?

Puzzled.