AxCrypt 1.x is deprecated, unmaintained and unsupported. Only version 2 has the sign in / sign out metaphor. With AxCrypt 1 you can check two options when entering the password – “remember this for decryption” and “remember this for encryption”. If you uncheck them, you’ll have to enter the password every time you do something. This is a bad idea, especially the “remember this for encryption”. Despite the dual verification entry of a passphrase for encryption, mistakes happen with data loss as a result. AxCrypt 2 removes this risk and is thus safer to use in this regard (as well as in all other regards…).
I really recommend that you switch to AxCrypt 2. It’s still free for equivalent use as AxCrypt 1, and is maintained and supported, and both more secure and safer to use.