Assuming you're talking about the diagonal belt across the hips, that is to support the sword; it is not critical to the integrity of the armor.
As to the other straps, as @Daniel says,
I think he's referring to the straps on the lower edge that hold the tassets in place and the ones front and back that hold the plackart and lower back piece. Given that the tasset straps were still being used in the 17th century on half armour there doesn't seem to have been much of an issue with these straps being cut. As for wear, these armours were maintained so straps starting to wear would be replaced before they could fail.