When you run Second Copy as a service the Local System Account used for the service may not have adequate permissions to access the network share.
Here is a suggestion to try:
Create a username on local and remote computers with same username and password. Then make sure that this username has full control to the source and the destination folders. Then login as that user and start Second Copy. Then uncheck the box "Start at log in" from the Edit | Options | Startup tab.
Then Exit Second Copy. Then set up the service for this username.