I had this same issue in Xcode 7.3. To solve it I performed the following:
Deleted the provisioning profile on the developer portal website.
Created a new development provisioning profile manually on the
portal website.
Added new profile in Xcode under Preferences ->
Accounts -> Apple ID -> View Details. Attempting to just click the
download button beside the new profile kept giving me an error. It
was only when I clicked "download all" at the bottom that it finally
downloaded and fixed everything.