Can you port forward to the 254 address and call it good? Set the Sling to 254. I believe it's a Sling issue and not your router. I keep the first 25 numbers 2-25 free for DHCP numbering of your laptop and cells connecting and needing an IP address. The 254 is high enough and the number I use. Make sure your available IP addresses go from 1-255 (or higher). Once you have the IP issue solved but not keeping it's connection I have another place for you to look.
If in warranty, call Sling and have it replaced.
Out of warranty, have the 3 capacitors visually inspected on the board and if needed replaced. Google "slingbox capacitor failure repair" I just fixed mine for $6 and it's working again. Two of the 3 were bad.