Maybe I don't understand how Slingboxes work, but the general concept of a "home DVR you can access from anywhere" doesn't seem to require that the vendor maintain a server or stay in business for that matter for the basic DVR and remote-viewing functionality to work.
Here's basically how Slingboxes work: you have a piece of hardware that is connected to your network and the A/V connections on your cable box (it even has pass-through ports); the box then digitizes and compresses the A/V stream being spit out of the cable box. You also have a small IR emitter (built in to later boxes) that relays remote control commands to the box. It's not exactly a "home DVR you can access from anywhere"; it's quite literally a device that streams whatever your set-top-box displays while allowing you to control it.
Now, one thing they've done well is making the device a bit "fool-proof" for the average user to use. Most people don't know what an IP address is, or how to look it up, or that it changes; it's not a problem for those of us who have been doing that type of stuff for years. So what they do is maintain servers that keeps track of your Slingbox's IP address; so you can access it without having to know anything but your slingbox ID. The servers don't just do that; but they are also capable of relaying a stream (at reduced quality), should some crazy firewall/double-NAT/other reason occur that your client can't directly connect to it. However, most of the time the boxes will attempt to set up a port-forward on your router through UPnP, if that fails, it will then attempt to blast through the router using UDP, then falling back to relay if that doesn't work. While I would almost buy the argument "we have to cover those costs", one could argue "no one is asking you to"; they've just basically built all that in to the product.
There is also the issue that, for a while; they were hosting additional bandwidth as playback had gone strictly to browser-embedded clients. They had a desktop application for a while; but discontinued it sometime around 2011 and the 2012 models weren't supported. The worst part about that was if your internet went down with the older boxes; the client application could still find them over the LAN and connect without any intervention from Sling. The browser method meant if your internet was down; or their servers went down...you were totally unable to watch the device at all (unless it was an older unit) They have a desktop program now...and I'm still not sure if they list it as being supported by anything except the latest models. But at this point, all they're really doing is pushing a minimal amount of bandwidth to tell the client where your boxes are. It may still be able to find local boxes without intervention from Sling, but I haven't tested it. In retrospect, using a device that wasn't connectable using standard software was a bad idea; at the same time...the $180 investment was *much* cheaper than buying the hardware necessary to digitize 1080i video over component and compress it to a high-efficiency video codec in realtime. I actually considered something like an HDHomeRun; but I'd have to cannibalize a cable box for it's CableCard or pay an extra I'm-not-even-sure-what-it-costs for a standalone cable card...which at the time my provider was not allowing self-install on...and didn't do installs for anything except home-theater-PCs.
But ultimately, you can still only go so far keeping people locked in; and while many of us put up with some of thier stupid stuff in the past...making us feel like we've got to pay them to watch our TV on hardware we bought from them is an insult.
"Free markets select for winning solutions." -- Eric S. Raymond