My case is different, I use hot spot for internet at home but take with me when travel. The router at home is still there but hotspot is removed. For that, I notice the Tablo stops recording within 24 hours. Even though I set recorded a week in advance. I guess, its brain went dead 24 hours if there is no internet.
If by chance you do not have a subscription for guide data
Tablo devices without an active subscription will download the guide data for the next 24 hours.
and would have not schedule beyond that. [source: https://www.tablotv.com/blog/tablo-faqs-do-i-need-internet-use-tablo-ota-dvr/]
Yes, for example, you can go to movies section and pick the movies you want to record a few days in advance. But then, it does not since it stops anyway within 24 hours of no internet connection.
If this is a non-internet related issue… Myself and other’s find this irritating and annoying. Despite the reading the box “To download guide data and stream HDTV out-of-home”
it’s misleading… Officially full-time always on internet access is required for tablo’s operation. There my be devices which function, for a time, with out it - or other work arounds… if you take away it’s internet, for tech support, you may be SOL. 
Recently had 2 day internet outage and when I tried to access the Tablo via my Roku, got a “no internet” error and no farther. Just when I wanted to access my recorded content, I couldn’t.
Seems like a no-brainer to be able to access my recorded content via my network when internet is down…
You should be able to continue after that warning.
What Roku OS version are you using?
“Recently had 2 day internet outage”
Did your DHCP server go down? And if so did your IP address lease time expire in those two days.
If so you are probably SOL since each device needs to re-establish it’s IP address lease at by the end of the lease time.
What you say "You should be able to continue after that warning. What Roku OS version are you using? " is exactly what we expect to happen. but it does not. That’s why we have this thread. In a perfect world, the shedule is good for 14 days (beta); I would expect to schedule the program I like a week from now. Now, my hotspot is removed (because the Tablo is at my vacation home) so I will come back to my vacation home in a month, but when I come back in a month, when I like to watch that show, it was not recorded. I don’t see why it makes sense because the time was already set, then just go ahead and record it just like any regular DVR. All it gives is frustration of the user. 
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