As you say – that’s not how it’s supposed to work, and something is definitely wrong if what you describe is what is happening.
There are a few cases where the offline / online password can get a little out of sync, but that only happens under specific circumstances and only when changing or resetting passwords.
1) Please follow the instructions here: https://www.axcrypt.net/blog/send-complete-error-report/ and send the result to support at axcrypt dot net, and mention it’s for me.
2) Start AxCrypt in normal online mode, use the “clear all settings and exit” option. Restart AxCrypt. Re-enter your AxCrypt ID email and password, sign in, verify it all works and then try the “always offline” option again.
Step 1) is to have information to analyze to try to determine the cause of the problem. Step 2) is to verify that offline actually does work. It does not fix the problem if there is one, causing you to get into that situation, but that’s what step 1) is for.