Greetings cme33,
Thanks for visiting the Apple Support Communities! I understand your Bluetooth speaker is disconnecting from your iPhone.
Nice job with the troubleshooting steps you've taken. Check for possible interference which may be causing the disconnects: Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support
If the behavior continues, then I suggest attempting to further isolate the behavior. To do so, test the Bluetooth speaker with a different device. If the issue persists with a different device, then I suggest reaching out to the Bluetooth manufacturer for assistance.
Additionally, test a different Bluetooth accessory with your iPhone. If multiple Bluetooth accessories disconnect from your iPhone, then I suggest reaching out to Apple Support, as outlined in the following article: If you can't connect a Bluetooth accessory to your iPhone, iPad, or iPod touch - Apple Support
"If you still have any of these issues, contact Apple Support:
- You can’t turn on Bluetooth or the setting is grayed out.
- You can’t connect any Bluetooth accessories with your device.
- The accessory manufacturer confirmed that your accessory is working correctly."
Kind regards.