I understand that you are having some issues while using a third-party power line.
As the first step, I recommend you to hook up the Slingbox directly into the router and test the connection. This test will allow you to determine if the issue is related to the Slingbox or any other network component.
As a second step, you can also power cycle the Slingbox PRO. You only need to unplug the Slingbox power adapter, wait about 5 seconds and plug it back.