Unfortunately, there is no method that we provide at this time to remotely reboot your Slingbox. I took a look in your account, and it looks like your Slingbox is currently offline.
Take a look at this article. It is the article you are directed to when you click "here" for more information, and it is a good place to start when you (or someone else) is with the actual Slingbox to troubleshoot.
Hope this helps!
It probably isn't any assistance to you right now, but I use a WeMo switch at the power outlet end of my Slingbox Pro-HD, which allows me to switch off and on, over the internet, and remedy some of the issues you mention as potential causes. I also have a switch of the video source too, so can run a power cycle on that, when necessary. The switches can be set up with "Rules", if you wanted to carry out a power cycle every few days/weeks, but personally, I prefer not to do that.
As these switches work over an internet connection, I haven't found a way of rebooting my broadband router, remotely, but thankfully, that hasn't been a real issue, to date.
There are many other styles and brands of remote power switches, but the WeMo works for us.
Do you have a friend or neighbour who might be able to run the power cycle for you?
Thanks, I guess I will have to add some remote power control for the sling box. I do have a remote power switch for the router that is controlled by a phone call (land line).
So I can reboot the router when there is no Internet connection.
It is by Black Box called the Power Mate item SW1070A and has many programmable features, but I could not find it on the Black Box web page. They have a ton of items so it is probably replaced by another style.