This is a huge bug, that so far Amazon is not able to help with. Mine also shows my Echo Dot as offline, even though I can ask it if it is online. It replies back immediately with "Yes, I am connected to the Internet". Since the Alexa App only shows offline, you cannot select many of the options, including Bluetooth. This is not specific to the app. It shows offline on iPhone app, windows 10 browser, and at customer support. My best guess is they can't get through my firewall, which is completely unacceptable for this level of connectivity. if I completely hard reset (volume down + microphone button for 20 second) it puts the device into reset, at which time I can connect the unit to a speaker. But even after, it shows the device as offline. This means I must hard reset to connect/toggle to any speaker. This is obviously a bug that Amazon is not admitting to.
I had the identical problem. The Echo Dot worked perfectly but showed "offline" on my mobile phone. This was an issue as I was unable to select the option to connect to my Bluetooth speaker while the Echo Dot showed "offline." This was simply resolved by resetting the Echo Dot by simultaneously holding down the mute and volume down buttons for about 10 seconds. (Until the lights started gyrating) Echo Dot simply asked that I go back into the App to set up an internet connection etc. I did notice that the original name I had given this Echo Dot location still existed and still showed offline. Echo Dot defaulted to a new Echo Dot profile, was online and functioning perfectly. I sure hope this help! Good luck.
You've encountered a limitation of the v1 API. We released a new API recently (v20160207) which addresses this issue and many more! I highly encourage you to check it out:
Microphone stopped working 2 Answers