During our recently completed TA on Constellation, the Celebrity Today warned us in advance that the internet speed would be especially poor during the middle stage of the crossing and it was--it was unusable for about a day and a half.
During that time I spent an hour in the iLounge using one of their iMacs to print out something. While there, I observed a steady stream of passengers coming to the iLounge asking about the internet outage ("when will it come back"?)and they all received some form of renumeration in the end without asking for it. The most common form was getting their Basic Wi-Fi package upgraded to Premium for free.
In fact a few passengers came to the iLounge to have their Elite minutes activated because they didn't know how. In each case the iLounge employee explained that the internet was not operating at the moment, but he would increase the number of free minutes that they would get because of the inconvenience.
So lesson learned, it does pay to go to the iLounge if you have a problem. The employees are motivated to keep all their customers happy--after all, aren't they subject to evaluation on the post cruise customer satisfaction survey? The ability to upgrade passenger's Wi-Fi packages or add minutes cost them nothing and I was impressed how often they resorted to it.