Our military might consider a 20 kiloton device which is going to only obtain a 12 KT yield to be a failure.
Al Queda may not.
Sorry about that, I had to go find a second source for the half-life information.
Roughly 53 days for the Berrylium trigger and about 12 years for the tritium booster.
Whether it fizzles or blows after those times are up would depend upon the speed of the projectile/trigger inside the gun-type weapon, along with some shape/form/purity questions (of the core as well as of the trigger), presuming that the electronics were still functional and that the conventional explosives were still viable after prolonged exposure to massive doses of radiation and shock, et al.