I mean the snare string then I guess! Because it's the snare wires that keep falling off
I can't imagine the force needed to knock the snare wires out of their solder!

Actually, I can't imagine you being a heavy hitter, even being a factor in the strings not staying in the strainer. It would more likely be the length of the strings, or tensioning of the strainer, or how tightly the screws are torqed in the strainer or butt plate.
Some snare wires have both holes and a slot on each end so you have the choice of using either strings or straps respectively. I always had more luck using straps made of folded-over "strapping tape" that is meant for wrapping packages for shipping. The metal grabs the softer plastic of this tape yet the tensile strength of the vertical pull is reinforced with those cellulose strands.It stays put, it lasts, and it's cheap.