(1) They were minarchist not anarchist, so not sure what your point is about government; they weren't looking to
re-invent government defense privately or some such, rather their failure mode was ultimately political alienation manifested in violence (rest of world in that area hated/afraid of the possible prospect of successful libertarians upsetting the status quo and thus called to action to squash them at once). They likely could have survived with the same weak military under a different more palatable political model that makes Australia and Tongans happy face, because in reality Aus+polynesia had no interest in actually taking the land
for themselves only expelling libertarians.
(2) Yes they were militarily weaker than the entire coalition of australia + polynesia under the flag of Tonga for invasion, this applies to pretty much all sovereign islands in the Pacific, there is no particularly special lesson to be learned here about polynesian military might -- even the Tongans were ultimately proxying Australia and would find the same fate if Australia disliked their political model.
(3) The takeaway Michael Oliver did actually learn (dude was a legit genius) from this is if you find any success "democratic" countries that preach tenants of peaceful property rights actually are just frauds running under the cold veneer of "whoever can kill and steal, gets the land."
(4) The next "adventure" by the same foundation used lethal force to defend themselves (Vemerena), and IIRC it did survive a bit longer. (There were three major attempts by Phoenix foundation, one was making a new island island, another a civil war-ish breakoff nation in Vanuatu, and another an attempt at civil democratic secession in the Bahamas-- the one defended by armed actors was arguably got the closest to success)
(5) Thus ultimately we can see the property rights model of modern democratic countries are no better than the founding libertarian models, it's just violently taking whatever you can get away with whenever you can get away with it wrapped up under more flowery language than what the libertarians used and with generally higher tax rates. We see this continually whether it is libertarians or communists, the bigger democratic countries will just fuck their shit up as a mode of political alienation whether they have a "government" or not.
(6) Conclusion is duration of survival of small territories of Minerva, communists, et al has little to do with their philosophical model of property rights. Has more to do with forming allies (Cuba with Russia for instance) and/or military might. None of which is philosophically incompatible with the Minervan model of minarchism.