Hi,
It has nothing to do with Asterisk. The Asterisk AMI is connected by the FOP2 Server, while the disconnection you see is from a browser to the FOP2 Server:
Asterisk <--> FOP2 Server <--> Browser
Your problem is on the right part of the above diagram.
If you see disconnections both from the Chrome Extension and the FOP2 page itself, then you definitely has some network issues between your browser and the FOP2 Server connection. Debug/Troubleshot unfortunately is not that simple, but I will give you some things to try:
1) Do you use HTTPS or HTTP? If you use HTTPS, did you configure the ssl certificates in fop2.cfg ? If not, you must do so in order for FOP2 to connect via secure websocket. One symptom of misconfigured ssl certificates when using HTTPS is that , in the FOP2 browser GUI (not the extension), it will take several attempts (perhaps up to a full minute in time) until it shows the login form to enter exten/password. Solution in this case is setup the ssl certificate and key files correctly in fop2.cfg, another option is not to connect via HTTPS
2) Check if the fop2_server is running well, if you restart it every minute, or if you reload asterisk every minute, it might cause all connected browsers/clients to disconnect.
Here is a link on how to debug FOP2, look at the javascript console mostly and see if you catch the error that causes the disconnection there.
http://support.asternic.biz/?/selfhelp/view-article/how-to-debug-fop2/10