Usually, after the Chromebit/Chromebox reboots, it should connect to the internet straight away. If it doesn't or showing as offline in Signage, it could be that the wifi signal is weak or is being blocked by the TV.
First, determine how far your device is located to the router. Is the device connected to the TV screen via the HDMI extender or is it hidden behind the screen? If so, that would one of the reasons for a poor WiFi signal. TVs have a lot of RF shielding in them and will likely block WiFi signals going to the attached device.
Please try to use the HDMI extension cable to position the Chromebit away from the back of the TV. See if you can improve the signal that way.
You can also check your Chromebit or Chromebox Wifi Signal using Chrome kiosk health monitoring tool in the Chrome device management console. Once you know the Wifi signal you may want to refer to this page to determine if your wifi signal is acceptable or if it needs improvement.