Many years ago a client brought in an alto saxophone for repair. The symptoms were common enough - it blew down to G and then no further, in either octave.
It didn't take a lot of thought to arrive at the conclusion that there was a leaky pad - on or around the G# ( this being the next note down).
However, upon examination I found the pads to be in excellent condition!

An octave key problem then - the G key links to the octave key mechanism, even a slight imbalance here could throw the notes, though not perhaps on the upper register.
But no, all was well here too.

I was perplexed, flummoxed even, and as the client was pushed for time he agreed to leave the instrument with me and collect it the next day.
So I put it to one side and carried on with the other work on the bench.

Later that day I picked up the saxophone again.
I looked it over once more, double checking those pads, working the octave key mechanism - but to no avail. Each time I blew the horn I got the same result...fine to G and then nothing, not even a whimper.

It was only when I lowered the horn to stand it on the workbench that I heard a most curious sound...a sort of clonk, followed by a faint whoosh and then a telling clunk!
Something had slipped down the bore!

I peered down the bell, and there, still wobbling gently in the bottom bow was....the mouthpiece cap!!
I was amazed! I turned the horn end up and watched as the cap slid neatly to just below the G tone hole and stuck fast. All that was required to free it was a gentle tap on the bottom bow.

The client called in the next day, and seeing a grin on my face asked me if I had found the solution to the sticky problem. I said I had - and incidentally had he lost a mouthpiece cap recently?
Yes he had, and how did I know???