tooltips – New features announcement / app cue

I am working on the announcement of new features for our existing portal users. The announcement will be made by displaying a distinctive modal element that is triggered by some specific events. Through this element, the user can either upgrade, get more info or close the modal by clicking a standard icon. The question is if there is any pattern/research about how many times this element can be displayed before the user considers it annoying? How insistent should we be promoting new features? I am sure you know what I am talking about :] Thanks in advance.