Ah, I understand now.
I bet the recording is one the Tablo's hard drive, but just not displaying its existance in the recordings section.
Tablo stores recordings on its hard drive in ~ 6 second segment files with a .ts extention.
You can check for recordings following the example in this post:
Any chance you're filtering out the recordings you expect to see?
I don't usually use my web browser to connect to my Tablo, but noticed the recordings section has multiple subsections: All; TV Shows; Movies; Sports; Manual.
On my Roku, I believe there are only 2 recordings sections: All; Recent Recordings.