I was having trouble with a RN4677 module, what was happening was the module is supposed to go into comand mode after receiving 3x '$' (or whatever the command mode escape charcter was, can't quite remember), however in receiving the first '$', it would wait for a second one, and when the second character was not a '$', it would discard whatever chunk of packet it had received the original '$' in.
This essentially made the module unusable. This was in BTC mode but I bet the same problem was in BLE mode. After much discussion with Microchip, they provided a firmware upgrade and everything works now.
So what I'm saying is, check if there is a firmware update for that module, especially if it is a microchip part. Pretty inexcusable to market a module with such a glaring error in what could be a really simple, robust algorithm for detecting command mode excapes!