How are you writing to the file?
(Assuming you are using one of the high-level File I/O VIs.) Make sure to keep the current filename in a shift register. If the file path is empty, you'll always get a dialog. Also wire a "true" to the "append?" terminal so the data is added to the end of the current file.
To save resources, you should probably use low-leve File I/O. Open the file for writing once outside the loop, then keep writing to it inside the loop. Close the file outside the loop when the VI stops.