I have an Autopiano Recordo which I believe has the same pump that
Jonathan Holmes describe in the 121007 MMD.  The straps I have are a
canvas/rubber belting material about 1/4 inch thick.  I measured the
stroke at the end of a bellows and found it to be 39 to 40 mm.  The 
bellows is closing when the belt is compressed, but in this state the
bellows is being exhausted.

When the bellows is opening, the bellows is extracting air from the
system and the straps are under tension.  If the straps are flexing too
much, it suggests to me that maybe the straps are at fault.  But it may
be that the external flap valve on each bellows is not opening easily
enough.

My pump was reconditioned about twenty-six years ago.

Paul Rumpf
Melbourne, Australia