This error message might look scary but it simply notifies you that your integration with QuickBooks has expired. Integrations expire once a year so you will be notified occasionally what happened.
To clear it you need to refresh your QuickBooks Online integration. Use the known path from the 'Account settings' menu, into the 'Integration' tab. From here click 'Change' and choose QuickBooks again.
Now you can try publishing your item(s) again although the error message may still appear.
Please don't disable the integration at any point during the process because the information about your Chart of Accounts and Payment methods will be lost.
If this is the case, you'd probably see 'Object not found' error.