We fixed it.
It was driving me crazy. We have two Chimano Steps DI2 bikes. If it is not humid they never showed any E20-E10 nor connection problem. However if the humidity increases, they popped up every 3 minutes. We saw two behaviours:
E20 / E10
Just sudden empty screen
I got an e-care...
Yes, the problem for me was solved by replacing the battery. Here is how we found out.
Got a testbattery from Shimano
Tried commuting with this battery, all was fine
Then they replaced the battery for free (still under guarantee)