BLE connection counter

From which side - central or peripheral?
If you're the central you are the one who initiates the connection, so you should be able to increment a counter when this happens.

EDIT:
From peripheral side there are events for connect and disconnect:
https://www.espruino.com/Reference#l_NRF_connect
https://www.espruino.com/Reference#l_NRF_disconnect

This example will flash the green LED on connect and the red on disconnect:

NRF.on('connect',()=>{
  digitalPulse(LED2,1,200);
});
NRF.on('disconnect',()=>{
  digitalPulse(LED1,1,200);
});

It's easy to try with just the WebIDE as connecting central.