Apple support does not officially provide steps for resetting your iPhone or iOS Bluetooth connection; however there is a reset you can perform to help troubleshoot problematic Bluetooth devices from connecting to your iPhone. If you already tried forgetting and re-pairing
1. Turn off Bluetooth on your iPhone Settings -> Bluetooth
2. Next, hold the sleep/wake button and volume down buttons until your iPhone displays the Apple logo. (Your iPhone will turn off and back on).
3. After your iPhone reboot completed, re-enable Bluetooth and see if this solved your connection issues.
If you still experience issues, reset your iPhone network settings. Go to Settings -> General -> Reset -> Reset Network Settings