It seems that you are having some issues with your Slingbox PRO-HD ever since you installed a new router.
Unfortunately, you did not include any information about your Actiontec router. This limitation prevent us from helping you to check and adjust some router settings in order to keep a steady connection.
In all case, we encourage you to contact your router provider and ask them if there's any kind of restriction or settings to adjust on the router that might be the root cause for this behavior.
Let us know about their response.