That is rather odd. Unless there is an error on their end. I would suggest that you try starting up the tablet in "Safe Mode" and uninstall the application from there. Then restart normally and see if it will allow for a fresh install. Should it give you the same issue, then either another app on the device is giving you problems, or the app creators are having issues with their app.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.