Hi Rodney,
Welcome back to the forum!
Thanks for the detailed explanation of your workflow. That helps a lot!
You’re right to mention that Reach M2 is current hungry. I wouldn’t put it this way, of course 
but it can be close: power requirements for M2 are stricter than for M+.
This is not the reason for the behavior you’re experiencing, though. Reach M2/M+ have to sync their time before they can be visible in the app. As @jp-drain-sol rightfully mentioned, there are two ways to do that: through satellites or via the Internet.
So your units have to have the GNSS antenna connected and the sky visible every time you turn it on. Alternatively, it’ll work just like it does for you: once the unit connects to the network with Internet access, it syncs the data. In both ways, the finish of this procedure is shown with a solid green LED.
So, the unit will be turning on just fine without any external networks if it sees the satellites. Just a quick tip here: it’s usually better and safer to switch the unit off in the app. That’s just a way of protecting the data on the units.