How long can you play a note on your saxophone?  One measure, four measures?

It depends on which note and the volume.  And a baritone sax takes more air than an alto sax.

Being able to play long enough to cover a whole phrase without breathing gives fluidity to the phrase and makes it sound better.

Kenny G holds the record for holding a note, but do you really need to play a note for longer than ten minutes?  Who wants to hear that?

Having good posture enables you to hold more air in your lungs.  I breath by making my stomach expand out when I play, like a baby does.  Herman Riley taught us that a few years back.

And doing long tones as part of your practice routine will get you some control over the notes as well as extending how long you can play.