Hello MsLouise,
Thanks for using Apple Support Communities! We see you're having an issue maintaining a Bluetooth connection, and we'd like to help.
You've done some good troubleshooting so far. Next, verify that interference is not causing the issue:
Resolve Wi-Fi and Bluetooth issues caused by wireless interference
In order to move forward, verify if the Bluetooth issue is with your iPhone or your Apple Watch. Connect a different Bluetooth device, such as a Bluetooth headset, to your iPhone to see if it also disconnects.
Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch
If no disconnect, then try with your Apple Watch:
Use AirPods and other Bluetooth accessories with Apple Watch
Service pages if you determine which device is not able to remain connected to any Bluetooth device:
Apple Watch Service and Repair
iPhone Repair and Service
Take care!