Alright a little more troubleshooting. If I have a Roku Streaming Stick already powered on and connected and then remove the WAN access the Streaming Stick retains an IP address and am able to access the Tablo. However if I power down or power up another Streaming Stick with the internet disconnected it will not get an IP address from the Router thus rendering the Roku useless for accessing the Tablo.
I did not try this with the Roku Ultra which uses ethernet. So not sure, in the Ultra case, how it will work if powering up.
So this seems to be more of an issue with the Roku hardware/software rather than the Tablo.
Edit to add: Just located a post in the Roku forums about this very subject. It appears a recent update may have caused this to occur with the Rokus