"Access Denied" when editing some content types but not others!

I log in as an administrator. All is fine. I view a page of a certain content type. Fine. When I click on the "Edit" tab, I immediately get an "Access Denied" error. If I refresh the page, the editing form appears fine. I can repeat this as many times as I want, just by clicking on the "View" and then "Edit" tabs.

Perplexingly, this only happens for certain content types, not others.

If I enable shib debugging, I see that when I get "Access Denied", the session variable looks like this:

$_SESSION:
Array
(
    [shib_auth_username] => [my username]
    [shib_auth_rolecache] => Array
        (
            [3] => administrator
            [1] => anonymous user
            [2] => authenticated user
        )

)

But when I refresh and am allowed access, it looks like this:

$_SESSION:
Array
(
    [shib_auth_username] => [my username]
    [shib_auth_rolecache] => Array
        (
            [3] => administrator
            [1] => anonymous user
            [2] => authenticated user
        )

    [shib_auth_authentication] => shib_auth
    [shib_auth_rolelog] => 1
)

Also, when I am denied access, there is no $user variable in the debug variables, but when I refresh the page $user is there.