Sorry to answer your question with questions but I need some more information. You posted this on the SL forum so I am assuming this is an SL screen. When you say window I am also assuming you mean the form.
Now for the questions. Is this a tab you added to an existing form through customization Manager or is it a tab on a custom form built with the SL toolkit? Is the tab in the main body of the form or on a sub-form of the main form?
Look at the properties of the tab object and make sure the tabmaxwidth property is set to 0.
I have built many SL forms with tabs with the maxtabwidth set to 0 and when I pull the form larger or maximize the form the tab grows with the form.