Symptoms

K2 fails to connect to all registered SharePoint group providers despite URLs are correct. The following error is logged in K2 host server log: "Error","IdentityService","64005","ResolvingException","IdentityService.ProviderCacheIdentity:GroupProvider.GetGroup","64005 Failed to resolve 'SP:DOMAINGroupProivderName': An unexpected failure was encountered when contacting SharePoint to get information from the group provider: Unable to connect to the remote server."
 

Diagnoses

Error message clearly indicates connectivity issues - "Unable to connect to the remote server" as target SharePoint is up and running and relevant site collections reach able by all users, this means that K2 service account likely has issues with proxy settings or somehow else prevented from accessing Share Point sites.

This can be easily verified by logging into K2 server using K2 service account and trying to access SP group providers URLs - if those are not reachable it makes sense to verify proxy settings configured in IE for K2 service account.
 

Resolution

Verify that K2 service account is able to reach group providers URLs and if it is not make sure that proxy server settings configured correctly for K2 service account.