I've got a couple of tubes that are several years old, and I would guess that they are good as long as the stuff stays liquid. It is essentially cellulose nitrate dissolved in a solvent that is basically acetone. As far as I can tell, it is a glue that dries, rather than curing, and it seems to work as long as the solvent is present.
It is far from the strongest glue around, but it is fine for patching a tear in a canoe's canvas, because it dries rapidly, is a bit flexible, and is waterproof (or for gluing plastic model airplanes together where it gets its strength by actually melting the plastic, creating a welded joint when the acetone dries off.)
The history of Ambroid can be found at
http://www.ottertooth.com/Canoe_pages/ambroid.htm, where it is reported that " Old-timers have told the Ambroid Company that it lasts for decades in the tubes."
As far as I know, it is no longer made -- but Devcon's Duco cement seems to be almost identical.