Hello Simon.   I reviewed your video on YouTube and immediately
understood your problem.  As two others have indicated, your bellows is
not holding the air enough as indicated.  It is also obvious from your
video that the pumping vane is in fact pumping air into the reservoir.

We have been covering bellows for the better part of 25 years and we
have a fixed routine that we go through, as follows.  Before covering
we check all four valves.  If they do not hold air, we replace them
with new valves.  Not all valves can be cleaned.  We have in fact
cleaned valves in ultrasonic cleaners with soapy water and have had
some success.

Once this is been established we then cover the reservoir.  Prior to
this, we have removed the whistle and cleaned the flat flap in the back
to make sure there is no dirt on the valve and it does not leak.

Once the reservoir is covered with the skin, we then check to see if
the reservoir holds air by pressing it by hand holding the dump valve
closed.  If it does, the zephyr skin bows out.  If not, we then take
soapy water and a small brush and check the glue joints of the skin to
the wood while the reservoir is under pressure.  The leaks become very
obvious and need to be re-glued.

We then cover the pumping side closest to the whistle.  After drying,
we then pump the half pumping section to ensure that the reservoir is
being filled.  Once that is established we cover the final section of
the pumping side and the job is complete.

The focus is on recovering reservoir.  If it does not hold air as
indicated, you have no hope of getting a good bellows.  If you require
additional instructions, give me a telephone call at 1-888-711-4646.

Sincerely,
Tony Ciuffini - The Musical Box Doctor
San Pedro, California
http://www.musicalspecialties.com/Repair/repair.html