Galaxy Nexus - Xiia use with Display off

I too have this bug. It seems to only happen when I'm streaming with WIFI on and the screen is off. I did a lot of research and discovered this post: http://forum.xda-developers.com/showthread.php?p=28477796#post28477796

There was a change in API 12 (Honeycomb and later) with the way "wifi lock" is handled. Even if the sleep policy in settings->wifi->advanced->"Keep wifi on during sleep" is set to "always", wifi will still be in a "low performance mode". This results in throttled speed (f.e: stuttering streaming), high latency (ping your phone) and can even cause disconnects, when the screen is off.

Still this is not bug but a feature of Android and should be addressed by any app that needs full wifi performance. Any app that needs full wifi performance (like streaming or file shearing over wifi) should call for "WIFI_MODE_FULL_HIGH_PERF". This can be found in the official "android developer reference ". Before API 12 (honeycomb) an app just needed to call WIFI_MODE_FULL for "wifi lock". If an app isn't coded proberly for honeycomb and ICS and has issue with Wifi performance appart from calling "wifi wake lock", you should report that to the developer of that app. 

I still found a simple workaround for scenarious in which this function is not properly called. There is an rather simple widget on google play called "WIFI High Performance Widget ". If the widget is enabled, the function WIFI_MODE_FULL_HIGH_PERF is called and the wifi performance is on full speed even when the screen is off. Im not in any way involved in the developement of this app and there might be other apps out there, that could achieve the same (for example: Android Terminal emulator  also calls WIFI_MODE_FULL_HIGH_PERF if "wifi lock" is enabled.) Still this widget is the simplest solution i found thus far. Just enable the widget and get full wifi performance when screen is off.

This seems to be the problem for me, as installing the app suggested in that forum, the problem has disappeared. I hope this helps you in solving this problem. It seems to only affect those with Honeycomb and later.