VS 2008 - Event Handler For Dynamically Created Button

I'm dynamically creating a table on my page with rows and controls. It looks like a gridview but it's not (it should've been, but too late now, seriously). I have a first name, last name, date of birth, etc. I want each row to have a button to add rows underneath it. So I create an event handler each time I create a new row and assign it to the click event of a button contained in the row. But it's not getting called.

Is it correct that the event handler doesn't stay established because the buttons are dynically created and are lost when the page posts back?

Code:
ImageButton addDependentButton = new ImageButton();
addDependentButton.ID = ADD_DEPENDENT_BUTTON_ID_BASE + currentSubscriberIDAsString;
addDependentButton.ImageUrl = "/Images/btnAdd.gif";
addDependentButton.Click += new System.Web.UI.ImageClickEventHandler(this.AddDependentButtonByRow_Click);
Control[] addDependentArray = { addDependentButton, addDependentDropDown };
WebControlUtilities.AddMultipleControlCellToRow(currentRow, addDependentArray, Constants.CSS_CLASS_TABLE_TEXT_NORMAL);