Thank you for asking!
Right now, web server access is mandatory the *first* time you install AxCrypt on a PC. Thereafter there is no need for Internet access, although we’ll use it if available to perform update checks and similar.
We’ll be adding some form of ‘escrow’ mode very soon for the specific scenario you describe. For now, you can always be assured by the fact that the full source code is available so if we should suddenly and unexpectedly fold, the source code is available via mechanisms that have no connection to us.
There is nothing really vital on the server as far as AxCrypt file encryption is concerned. We do create and backup key pairs there, but they are for convenience – it’s not required for file decryption. In the end, all that’s needed is AxCrypt and to know the password used when the most recent encryption occurred .