Your leather straps originate from Latigo straps found in ranching. And just like any leather used on the ranch, they need to be cleaned and oiled regularly to keep them soft, supple and strong.
See the cracks in this photo? That’s from years of neglecting the leather straps. Eventually, the straps will break at those cracked locations.
To prevent this and keep your straps comfortably supple, use Saddle Soap (link, here) on a quarterly basis.