We are having the exact same problem with our slingbox pro hd, they work on the same subnet but any other internal subnet the networking is broken, it appears that the slingbox pro hd's don't observe the default gateway even though you set one.
My co-worker is currently on the phone with their support.
I just got off the phone with sling media support and after two hours of demonstrating this problem their technician told me that my corporate network is an unsupported environment and the sling boxes aren't designed to work with this type of network.
The technician wasn't even interested in logging this as a problem or escalating this to a higher level of support, I guess we'll return the 4 slingbox pro hd's we purchased and look for another vendor for our media rebroadcasting hardware.
We are also experiencing the exact same problem you are with Slingbox HD Pros. They become unreachable if we are not on the same subnet as the slingbox. We are a software company that works with cable boxes so we have purchased a wide variety of slingboxes and we can never get the sling hd pros to function as expected.
However, interestingly enough, when we use the Slingbox SOLO in the same configuration, they work just fine. We are able to access the SOLO's from any other routable subnet. It is extremely strange and must be some kind of software issue with the HD Pro's. I would love to report this to their Tech Support, but I've had similar experiences with them seeming to not care very much and giving me the same response of "The slingbox is not supported on that type of network." Well, I proved that it is with the Slingbox SOLO .
Hope this helps you out.