244Pu is the most stable plutonium isotope with a half-life of 8.08 x 107 years. Since the isotope is an even/even nucleus, the ground state spin and parity is 0+. It will either decay via spontaneous fission or alpha decay to a 0+ or 2+ state in the daughter. None of the decay modes is strongly forbidden. The 0+ to 0+ decay is allowed, in fact. Furthermore, if you accept the shell model at face value, then the last proton level for 244Pu would be a partially filled 2f7/2 with 2 protons whereas 240U would have a filled 1h9/2 highest level. For neutrons, 244Pu would have a partially filled 1i11/2 while in 240U the same level would be half-filled. I assume that a nucleus with a filled level is more stable then one with a partially filled level, although I am not entirely sure about how partially filled levels compare to half-filled ones.
Most of that points to a quick decaying 244Pu, so why is it so stable?
One answer could be that the high N/Z ratio for the nucleus decreases the probability of finding a formed alpha particle in the nucleus. The decreased charge density at the surface compared to other Pu isotopes will also lead to a lower alpha energy of the emitted alpha. Both of these factors should result in an increase in the half-life.
Likely it is the combination of many factors. Any ideas what else to include?