Why didn't it last?
I've been told it was because it didn't make the central government strong enough, but that sounds bogus.
What's the Libertarian explanation for it?
Basically, there was nothing stopping the states from printing up however much money they wanted in order to pay off the debts they incurred during the Revolutionary War. Hyperinflation ruined the economy and the call went out for a new convention to rewrite the articles.
Well by not making the central government strong enough, what they probably mean is that it didn't adequate provide for common defense, which is true. Shay's Rebellion was a real wake-up call that the Confederacy was simply unable to adequately protect life and property against insurrections. Of course, the root cause of Shay's Rebellion was the national debt the states had incurred while fighting the Revolution, and the Articles didn't really provide a way for the government to pay that debt. Add to that the states were printing money like crazy, so the currency was rapidly devaluing. Furthermore, the government could not adequately protect its borders, which depressed land speculation. Also, while the Articles severely limited national power, it was in essence too Democratic in that there was no effective bill of rights, and the states had too much power, so the basic human rights that the war had been about could essentially be stripped by a popularity vote. So you had congregationalist majority persecuting non-congregationalist churches, like in Danbury. Finally, the Articles really didn't provide any method with which they could be revised which meant that the whole thing pretty much had to be scrapped.
Which leads me to believe that a big problem was the establishment of the municipal states (MD, VA, etc) in the first place.