We seem to be conflating sword societies and paper. The original question asked about the survival of sword societies and provided a timeframe - in the near future (presumably). However, that is only an assumption, as we do not know whether paper will be phased out in the near term or medium term. Arguably, it is a moot point in the long term. Therefore, we need to go back to basics and focus on whether sword societies will survive.
This is a difficult question. Theoretically, they should, as long as the hobby and collecting interests persist. However, an alternative theory is that they become much looser associations of individuals, on a much more federated (as opposed to centralised) and possibly purely, or largely, virtual basis. If people feel sword societies bring benefits (educational, emotional, etc), they should survive as the members will persevere to sustain these organisations. However, if sword societies become irrelevant (through obsolescence of ideas, education, unavailability of study materials etc), then the threat of oblivion is very real.
Another stream of analysis, which posters often digress into, is how best to study - with swords in hand, electronically (photos on a website or other repository), by reading books (physical or electronic). Again, this is a different topic entirely and merits its own debate. In my view, study should be multifarious and variegated - physical, electronic, by virtue of passive information absorption (reading/listening) and active participation (kantei, debates).
Once, we abstract the method of information provision and internalisation as described above, as long as sword societies provide the avenues for learning or enjoyment, I hope they will survive. As Paul has outlined regarding the U.K. and as far as I know the US NBTHK are also doing, combinations of physical meetings, electronic videoconferences, printed materials, electronic materials, debates etc energise and excite the membership and retain it.
in my view, membership retention is one serious challenge. People often sign up but fall away as: personal conflicts arise, member aspirations are not met (these societies are not museums with vast collections and are not universities with dedicated teaching materials and courses; funds are not unlimited; volunteers donate their own free time for others’ benefit; societies cannot provide definitive answers members sometimes seek and definitely cannot shortcut hard work and learning) and sometimes members just join for the wrong reasons.
Another challenges are the age and sex factors: middle-aged and ageing males predominate. So, we need to diversify our membership bases by being more inclusive, more pluralistic and democratic in our outreach to prospective members, more tolerant and broad in subjects we cover (tosogu, kodogu, blades, restoration etc).
There is much more to say but this is such a vast topic that has often preoccupied my mind. We try to recruit and supplant membership decreases but my observations across several societies are that we are barely maintaining membership. We are not expanding or growing and we just about manage to stay at the same size. Other societies just fold and disappear.