Notes added to a shape, with the View menu's Note command (or by selecting the shape and pressing the F6 key), will not automatically print. You must first tell iGrafx to output shape notes.
To get shape notes to display, from the File menu, choose Page Setup. Click on the Options tab of the Page Setup dialog box. Check the box that indicates Notes should be printed. You may optionally indicate shape text should be shown. If you have shown shape numbers, those will also be used in the Note information.
Please note that Publish is different than printing. Only PDF and HTML publish formats will display the Note. Publish to Word and PowerPoint are more like a copy/paste of the diagram picture, and will not show Note information, even if you have chosen to print Note information in Page Setup.