SQL 2012 - The remote server does not exist, or has not been designated as a valid Publisher, or you may not have permission to see available Publishers.

Step 1: Check the Log Reader agent account
Step 2: Agent account must be owner, If not make him DB_OWNER
Step 3: This will resolve in the next synchronization

OR

Step 1:  Check SQL Agent is Local System
Step 2:  Log Reader agent running under Impersonate Account
Step 3:  Change the SQL Agent to Some other account which has access
Step 4:  The Step3 will restart Agent, Once Its UP in next synchronization data will be in sync.