Does the server have any Service packs installed (SP). there are a couple of REST admin related issues fixed in SP1. If the server does not have any service packs installed you could try after installing the latest SP.
NIM058968 - Cannot login to REST admin if the url to REST admin login page is a redirected from a http endpoint to https.
NIM059442 - Domain accounts cannot log in to REST admin (a) when the server is off the network or (b) when the server is on the network but on a sub-domain and the SOM owner is a local account.