Hi Yota,
Normally when sharing notebooks via OneNote there won't be a expiration time.
But if the notebook was shared via OneDrive, the owner might have set a expiration time and as well as a password.
To check whether this meets your scenario, you could sign in OneDrive with the account who owns the notebook, select it then click details->Manage access, then click ... behind the link

But I suggest you use another direct way to check permissions:

Click Advanced in Manage Access page, then click Check permissions and input the email account to see if they still have permissions to the notebook.
If not, please share the notebook again. Sorry for the inconvenience caused by this issue.
And if it doesn't meet your scenario, in check permission page they have permission but they cannot access the notebook.
Please provide me a screenshot of the error message they received and the manage permission page.
For further assistance, please feel free to post back when you are convenient.
Best Regards,
Oliver