With H-shem's help, we have begun learning Hilchot Tzitzit with the Ben Ish Chai, Hacham Yosef Hayyim of Baghdad. The sefer is translated by Shmuel Hiley and published by Yeshivath Ahavath Shalom Publications in Jerusalem 5765/2005. He calls the names of the Chapters by the names of Parashiot, so instead of Chapter One, the first chapter is called Parashath Bereshith, Laws of Ziziyoth. Please note these are for learning purposes only. For the halacha lemaaseh, i.e. for what to do yourself please ask your own Rav.
Parashath Bereshith, Laws of Ziziyoth, Page 9: This is a long entry so we will break it up over a few days, BE"H
10 (continued). However, if one were standing on a balcony, and the tallith falls from there into the courtyard below, and one has to go and get it, or to signal to others to retrieve it, thus causing a long delay, and possible distraction, between the berachah and the action of putting on the tallith, there are grounds to rule that one may recite the berachah again. Nevertheless, after taking into account the severity of pronouncing G-d's name in the berachah, when it could possibly not be necessary, I would be inclined to rule that it is preferable to refrain from repeating the berachah. It would be a good idea, however, to recite the berachah in one's mind, without pronouncing the words out loud.
[Odh Yosef Hai (3) If the tallith slips off completely, one must repeat the berachah, when one puts it back on again. If it did not fall off completely, one should not repeat the berachah, when putting it back on.
The Poseqim HaAharonim write that, if the tallith falls off when one was praying the amidah, and others picked it up and covered one with it, one should touch the zizith and recite the berachah, after concluding the prayer.
This learning should be in memory of Maran, HaRav HaGaon Ovadia Yosef, ztz'l.