If you want to know how long it lasts, it depends on several things, first of all the "standard Drop" will happen after like 15 Minutes if I am not that wrong (not that I checked the clock for this) but the Dream Eater Sheep has an Attack which can rise your Drop Meter, also the Frog Dream Eater.
Standard is 1.0 but if it gets higher, the Gauge will deplete a bit faster.
BUT there are some Items to refresh the Drop Gauge, Morning Bell and Morning Alarm, the Bell Item will refresh 50% of the Drop Gauge while the Alarm will refresh the Gauge completely and reduce the Drop Speed. Same goes for Elixir and Last Elixir, doing the same.
Sora also has the possibility to Refresh the Gauge by the Command "Break Time", but its a chance of 1 to 3 to activate this.
So you can actually "play" with one Character for Hours, as long as you have those Items to refresh this once for a while, I played it like this, it was nice to give the next Character 999 Drop Points for all those Bonuses