Hi Derek,
That appears to be a bug in the current version 2.3.8.5, it should allow persistent logins with ldap.
As a workaround you can check the box to enable fallback to database auth, save site settings then check the box to allow persistent cookies then uncheck the box for fallback to database auth and save again.
I will fix that for the next release.
Note also that the duration of persistent cookies has been shortened to 2 weeks by default though you can set it higher by the timeout setting on the <forms element in Web.config
Best,
Joe