I understand that you are having some issues with the connection through the SlingLinks.
The first recommendation is to hook up the Slingbox directly into the router. This test will allow you to narrow down the possible root causes for this issue. It will allow you to determine if the issue is related to the Slingbox or the SlingLinks connectivity.
Even though you have applied some tests, I recommend you to check the following links in order to apply some troubleshooting steps:
Finally, if you are using the Slingbox SOLO, I encourage you to check this link and follow the included steps:
Hope this helps.