When you face “There’s a problem saving this record. You might not have permission to edit it, or it might have been deleted or archived. Contact your administrator for help.” issue/exception, check the following:

1. Check whether the user’s profile have Edit access on this object.

2. Check whether the user have proper sharing rules or OWD is public read write to edit the other users records. If the record is owned by user in higher hierarchy, then the user won’t be able to update the record.

3. Set debug log and find whether 1 and 2 and impacted on other objects through triggers.