Hmm, mine is working fine, so let's see if you can clear the problems. I have a couple of Taps, so I first needed to get one going again w/BT, so I went into BT settings of Tap.(I also had my iPhone playing a music app called Slacker thru the phone speaker.) Since I had not used this setup for a while, I just tapped on pair BT in Alexa app, and was told to turn on phone BT, and go into phone setting and look for which Amazon BT signal to connect to. I did, and the two devices were paired/connected right away. After listening to Tap a while I told Tap to disconnect BT. It did not auto connect to phone again. I turned off phone BT, and in a moment I turned it back on again. I then told Tap to connect BT, it did so and the music was playing again.
They have been playing together for quite a while now with no issues. If you are having issues, do what should be done with any device acting up. Reboot it. In case you don't know how to reboot the Tap, you must hold in the Power button on back for around 3 seconds; until it omits 3 beeps and goes into complete shut down mode. After a few seconds press in the power button and unit will restart from scratch, including reconnecting to the router. This is how I always turn off my Tap; otherwise, just pressing in the power button briefly just puts the Tap in standby and batteries can run down; they won't with the complete shut down.
Also, if you know how to completely reboot your phone, do this too at the same time you reboot the Tap.
Let us know how it all goes for you. Good luck.