My tefillin shel yad came with a cover on it that I think is for protecting its squareness. The problem is, the cover isn't tight against the bayit, so it ends up falling off. Any simple tips to prevent that?
A good solution is this product. It stays firmly on the bayis of the shel yad, and won't come off awkwardly in the middle of Shacharis when you move the wrong way! ;) Here is a description of the product from the link I provided:
Rubber tefillin cover protects the Shel Yad from being damaged or worn through contact with clothing, bumping, etc. Designed to protect the tefillin corners, and help maintain their shape and squareness. Stays in place on almost any size tefillin (32-36 mm). According to Rabbi Asher Weiss, the Kisu Yad is a hiddur mitzvah and a worthy innovation. This simple, patented device offers a solution for the issue of "roeh es ha'avir" (see Sanhedrin 89a). Rabbi Mordechai Eliyahu zt"l held that one should remove the plastic cover when reciting the brachah, but upon seeing the Kisu Yad remarked, "You don't even have to remove it when you say Birkat Tefillin."
[Special thanks to Ben's Tallit Shop at tzitzit.tallit-shop.com]