TL:DR If your echo devices won't connect check to see if parental controls are blocking websites like fireoscaptiveportal etc. preventing them from authenticating with Amazon. 

This is to save anyone that was having the same problems I was. I had 2 Amazon echo dots that seemingly randomly dropped off my mesh network. They worked fine for about a week after I got my deco and then randomly wouldn't connect. I troubleshoot with Amazon for about 3 hours to no avail. Finally they gave me a discount code to buy new echo devices so I did. Those arrived and almost immediately started having the same problem. Meanwhile I have 4 other echo devices working perfectly on the same network. 
 

I thought to myself "why are these devices different?" The only answer I could come up with was that I had added them to my kids profile since they're in the kids bedrooms. So I go to the profile and I see blocked websites in history coming from them (I know it's then because these are the only devices in my kids profile right now). Sites like fireoscaptiveportal, acscaptiveportal and other things that sound Amazon related. Parental controls are preventing the echo from authenticating with Amazon.

I remove the devices from the kids profiles and boom. Immediately see traffic flow. Go into the Alexa app and the devices which have been showing "device unresponsive" now show "Online". Test a voice command and it works right away. Sigh of relief and also disgust because I paid eighty dollars for two new devices when I could have just done this from the beginning with a little more analytical thinking.