Do I have to paint a picture? How many lightly guarded neutron sources do you think there are in the US? How many research labs, hospitals, etc., where the stuff is ready to be used? The day you hear about a theft from such a place - but by then it would be too late.
But aside from that, suppose you need 1 pound. Start with 4 pounds and you have effectively tripled the half-life. Start with eight pounds and you have quadrupled the half-life. Since the actual required amounts are significantly less, it gets proportionately easier. Po-210 decay products can be separated from the remaining polonium through chemical and physical processes when such separation is desired. Since the half-life of polonium-210 is 138 days, the hypothetical 8x supply would last for a year and a half. So the trick isn't really to get exactly the right amount, but to get enough of the right stuff so that you have as much time as you need for the operation. From Iran or Pakistan or North Korea or Cuba or Venezuela or China or Vietnam or France or South Africa or Libya or ...
"But aside from that, suppose you need 1 pound. Start with 4 pounds and you have effectively tripled the half-life. Po-210 decay products can be separated from the remaining polonium through chemical and physical processes when such separation is desired. Since the half-life of polonium-210 is 138 days, the hypothetical 8x supply would last for a year and a half." - calenel
Not inside your weapon. What you are saying is correct for high school physics experiments, but it is incorrect for atomic physics packages due to purity issues. Put simply, you no longer have a pure source, and can't readily identify what is pure or impure (inside your weapon) after one half-life cycle has expired.
Your overall neutron emission rate will no longer be precise, as some neutrons will be absorbed or radiated at different times by the impurities that time introduces.
Plutonium 241 (commonly found in Pu-239) rapidly decays into Americium 241, for example...a problematic Gamma emitter.
Po-210, for instance, does an Alpha decay into lead...a neutron shield. So simply tripling your quantity of Po-210 can't triple your half-life (or effective weapon life) because you are introducing a lead shield into your fissionables in your physics package itself as Po-210 decays over 140 days!
The way around this natural time limit is *maintenance*. Lots and lots of highly advanced clean-room maintenance (by highly skilled personnel) who understand that Plutonium is pyrophoric, brittle, and oxidizes rapidly.
These are not things that are done out in the field. You don't distill plutonium out in the field. You don't machine it out in the field. Nor do you create meaningful supplies of Po-210 out in the field (you need a working nuclear reactor for that).