Different pages respond differently

I have two nodes, both of which are content type Page. I have a user with a specified role to be able to edit the Page content type.

I am using the Content Access module with the Role Based Access control settings. When the user is logged in, for one node the user gets the "Edit" option, for the other node he does not. Some rummaging about on the web site shows that what the user can (or cannot) access is apparently random. If I create a new node content type "Page" the user can edit it.

I had "Enable per content node access control settings" enabled as well, but disabling it made no change in behavior.

I'm not running any other access control modules, although I have in the past had the ACL module installed and enabled.