We have tried to recreate the same scenario with our local environment. But not able to recreate the same.
Please try to clear the AxCrypt local contents by clicking the Reset button in the sign-in dialog or via the AxCrypt file menu File | Options | Clear All Settings & Restart.
Now log-in to the AxCrypt app with the latest(new) password. then you can activate the offline mode.
You have enabled the option Always Offline( File |Option |Always offline). Then check installed AxCrypt app changes to offline. Now you can use the AxCrypt app in offline.
Still, you are facing any issue, please provide detailed information about the issue and write a mail to firstname.lastname@example.org. We are happy to help you.