A Stitch in time saves nine.

Not so long ago people had to make do and mend. Clothes were more expensive and had to be repaired with needle and thread. If a tear is caught quickly it doesn't rip further. So the wisdom here is to tackle a small problem at the outset before it develops into a bigger one. Put another way: "nip it in the bud". It is often applied to people's relationships: saying "sorry" quickly can prevent a lengthy quarrel developing.