The Gemara in Menachot 35b-36a establishes the foundational principle governing a torn tefillin strap: drawing from Devarim 6:8's word *ukshartam*, Rav Yosef rules that the binding must be complete and whole — a makeshift knot does not suffice — and Rav Ashi further rules that a sewn repair is acceptable so long as the stitching is not visible from the outside, deferring to common practice.
The Shulchan Arukh (Orach Chayim 25:4) extends this concern to displacement during wear: if tefillin slip from their proper place and must be adjusted, a new blessing is required upon returning them, though if one did not divert his attention from them throughout, the case is treated more leniently.
Underlying these practical rulings is the theological weight Berakhot 6a assigns to tefillin: they are called a source of strength for Israel because God's name is called upon the wearer through them, which explains why the Rambam (Mishneh Torah, Tefillin 4:1–15) demands that a person touch his tefillin continuously while wearing them and never divert his attention even for a moment, given that their holiness exceeds even that of the tzitz.
The Rambam (Mishneh Torah, Tefillin 1:1–4) grounds the strictness of all these requirements in the fact that tefillin's ten foundational rules are all halachot transmitted to Moshe at Sinai, each one indispensable — so that even a single point of a single letter that is imperfect invalidates the entire set.