The most common reason for this is if you already own the No-Ads feature. That feature always gives you the maximum TV Time bonus. There would be no benefit to watching more ads, so we don't let you waste your time doing so. You can learn more here.
The button will also gray out if you don't own the No-Ads feature but have watched enough ads to reach the maximum TV Time bonus. You only have this temporarily, so after it expires the Watch button should be usable again.
Finally, the Watch button may be grayed out if the game detects that no ads are available at the current time (e.g., if you're offline or if there are no ads to show at the moment). This should also be a temporary situation, so eventually it should become enabled again.