It might be a long shot here, but I would like to suggest simply: insum & absum
This is somewhat lax/figurative usage, but this sometimes happens in other living languages, that a common word is simply adapted to denote another meaning. Not sure I'm correct here, but consider example on/off for electronic device.
Got this idea from ephemeris site, ...
One of the things I love about Latin is how it is often so much more concrete than English. Going with that, and thinking of interrete (internet) as a literal net, I wonder whether intra interrete (online) and extra interrete (offline) would work.
Per Sabbata extra rete eram, sed nunc infra sum.
(On Saturday I was offline, but now I'm on....
For “online” you could say:
colligatus (from colligare)
conexus (from conectere, note: long o, single n!)
Thus for “offline” you could say:
Or you could go a different route and say:
seiunctus (from seiungere), or alternatively:
disiunctus (from disiungere)
These would be technical terms describing the state of a software program ...