Rashi explains that there is a concern that a small amount of the sewing thread may remain after the repair. A person might then add an additional seven strings, thinking that this would bring the total to eight tzitzis strings. However, the string which was a remainder of the sewing thread is invalid, since it was not put into place for the sake of the mitzvah. According to this view, the issue would only apply to threads which are used for sewing and only to the spot on the garment where it is proper to affix tzitzis. The prohibition would apply to any size rip.
[שו"ע טו, ד, משנ"ב י-יא, וביה"ל ד"ה ולטעם, וד"ה בחוטי; וראה שו"ע יא, ט]