I know this is really late, but I just updated my DroidTV app today, so this problem is new to me.
I noticed I wasn't downloading any of my shows, then yesterday when I opened the app, I was shown a promt screen that said my version was obsolete, and I needed to update it. There was a link to click on the screen, but it didn't work. I emailed their support, explaning my problem, and got a reply the next day(today). They included a file with the new version in the email, which I simply downloaded. I uninstalled my old version first, then when I found the new one in my files folder and tapped it, I was prompted to install it. Make sure your install settings are still set to allow programs not from the Play Store to be installed. After that, it went through an initial install that took about 10 minutes or so, and all my shows I had already downloaded were available again, plus the ones I had been missing.
This is one of the few subscription apps I use, and it's great for the most part. Occasionally some videos are incorrectly labled, and sometimes the video quality is poor, even watching on a small phone screen, but I've been able to keep up with some shows that I otherwise would not have been able to watch.