I would suggest trying the loopback connection to see if it works without an autopilot involved.
My guess is that the problem you have is the signal from the 3DR Radio are 3v3 compatible. This means the should work to trigger 5V TTL signals that the level convertor needs, but not always. I have had the same issue with the SparkFun Xbee adapter as well. The solution is to bypass the level convertor in the adapter board as the 3DR Radio and the XBee are 3v3 compliant devices.
If you cannot get it fixed by bypassing, I’ll send you ESP8266 with the MAVESP8266 FW on it.