I recently purchased a Google Chromecast with Google TV and have had multiple issues with Wi-Fi connecting correctly as well as failed updates.
After digging my way down the rabbit hole, I believe there is an issue with the NTP settings on the device and how it pulls the information from the network router.
Solution: Manually set the NTP time and date on the Chromecast with Google TV or Change Router default NTP Server.
Step 1: Select the signed in user icon in the top right corner
Step 2: Select the settings option on the blade that pops out on the right side of the screen.
Step 3: Scroll down the list of settings options and select “system”.
Step 4: Scroll down to the “Date & Time” settings option and select it.
Step 5: Select the “Automatic date & time” option.
Step 6: Change the setting from “Use network-provided time” to “Off”.
Step 7: Manually set the date and time to match you network / local time.
Step 8: Press the home button on the remote and re-attempt to sign into Wi-Fi.
Step 9: Wi-Fi that was formerly connected but showed limited connectivity should now work – Also Updates should also now work.
Step 10: Alternatively I wound up changing my routers default NTP server from the router manufacturer to googles NTP server at time.google.com and set the Chromecast with Google TV back to using network-provided time and everything started working correctly. I am not sure if it is a Google issue or default router NTP server issue but this resolved all of the challenges that I was experiencing.
Good luck on your adventure – I hope this helps!