I think a much bigger problem than old software on 32 bit machines is the fact that some (binary) protocols use 32 bit integers to encode dates. That means that even when hardware and OSes get updated and even if servers or clients are maintained, stuff will still go wrong when the protocols are wrong.
So keeping up to date software might not be enough. We'll also have to pressure our peers to update and to adapt new protocol versions (that might have other changes in addition to just the widening of the timestamps)
As long as you're able to update the software, it's easy to reinterpret the protocol as unsigned and get most of a century of extra time to worry about it. I don't think that's as big of a problem.
Heck, you can let it wrap forever and interpret timestamps as 'now plus or minus 50 years'.
So keeping up to date software might not be enough. We'll also have to pressure our peers to update and to adapt new protocol versions (that might have other changes in addition to just the widening of the timestamps)