The web player is not as smart as the standalone app when it comes to your Slingbox directory. I've found that it can find my Slingbox from the Slingbox ID but not from the IP address. I have to keep 3 different versions of the same Slingbox in my directory for when I connect from different locations and with different versions of the crappy Slingplayer software.
So try adding your Slingbox as an second device using the IP address and port number instad of the Slingbox ID. Or, if your directory already has it that way, try adding it again using the Slingbox ID instead.