Hi,  It appears that this music box is missing part or all of the
Geneva stop parts.  Its purpose is to limit the amount the spring is
wound.  Most importantly, it stops you from over-winding the spring
and it also limits how much the spring will unwind so that the disk
will stop turning while there is still enough energy in the spring to
play the disk properly.

The latter is your problem.  As the spring gets weaker and weaker, it
has trouble turning the disk.  It can play one or two notes together
but it doesn't have the strength to play multiple notes.  So it soon
comes to a staggering stop.

I don't think I've ever seen a music box that didn't have a Geneva
stop.  Sometimes the male part is missing, sometimes the female part
is missing, sometimes both are missing.  More commonly, the finger on
the male part is broken off.  Usually there is a square section on the
shaft of the main spring barrel, right next to the side of the spring
barrel.  And, of course, there should be a hole in the side of the
spring barrel where the female part was screwed on.

Be careful that the spring is completely unwound before you mess with
it.  If you unscrew the governor while it's partly wound, you can get
a very painful and expensive surprise.

Regards,
Craig Smith