Here are some troubleshooting steps you can try:
1. Update the firmware of both your Beats Studio 3 headphones and your Sony Smart TV. Updating to the latest firmware can help to resolve compatibility or connectivity issues.
2. Clearing the Bluetooth pairing list on your headphones. To do this, press and hold the power button for 10 seconds until the LED light flashes. This will clear the Bluetooth pairing list, and you can try pairing your headphones to the TV again.
3. Check if there are other Bluetooth devices in the near vicinity that might be causing interference. Removing or turning off such devices may resolve the connectivity issue.
4. If possible, test your headphones with another Bluetooth-enabled device (e.g., a smartphone or tablet) to see if the issue persists. This can help determine if the issue is related to the headphones or the TV.
5. If your Sony Smart TV has a "Bluetooth mode" in its settings, try toggling it on and off to refresh the Bluetooth connection.
6. Ensure your TV's audio output settings are set to "Bluetooth" or "Audio system" instead of "TV speakers," as this could cause the headphones to disconnect if not set correctly.
If you've tried all these steps and the issue persists, it might be a hardware problem or a compatibility issue between the devices. In this case, you may want to contact Apple and Sony customer support for further assistance. For Apple, just use the "Support" link on the bottom left-hand side of this forum's web page.