This situation could be caused by several different problems. The most common one is that you might not have a decent Internet connection. Make sure that other applications, such as your browser, can go online without trouble to rule out that it has anything to do with your connection. Sometimes, the signal of a WiFi network can be too weak to connect appropriately.
Once we’ve ruled out connection problems, it could be due to an application error. Maybe due to the shutdown of the app’s system or our own operating system, the application might not work properly. In the case, we advise you to uninstall the app and download and reinstall the APK. On the other hand, that also guarantees that we’ll be using the latest and most updated version.
Another problem that’s way beyond our reach is that YouTube may have blocked the use of TubeMate on its site. That wouldn’t be too unusual as it happens with other apps. In that case, you’d have to wait for the developers to come up with a solution and some news about the status of their service.
Bear in mind that the conditions of use of the video portal don’t allow us to download any of the contents thereby hosted. You’ve probably realized that apps to download videos from YouTube don’t last too long on Google Play before they’re removed (TubeMate, for instance, can’t be found on the official Android market). In any case, it doesn’t look like they’re achieving too much with this measure because there are hundreds of different mobile apps, software for PC and macOS, and web services that allow us to do so.