Instead of using the stable esp8266 package from esp8266.com I'm now using the staging version, based on SDK 1.3.0.
http://arduino.esp8266.com/staging/pack ... index.json
I am pinging since my last reply and the answer times are stable between 2ms and 5ms. No package loss so far!!
I cross-checked against another ESP01, flashed with the stable version (SDK 1.2.0), and the connection broke down after 10 seconds!