Make sure you are getting good quality fabric. Durable linen sheets will be thick, tightly woven, & use longer linen fibers.

I've never had sheets wear out or break like that, even the cheapest set I ever bought lasted 4 years. So I wonder how you are washing them? If you have a top loading washer your sheets may be getting wrapped around those awful center agitators and ripping. You may need to try a different gentler setting or just wash them by hand.

Never ever put linen or cotton sheets in a dryer either, hang them to dry if you want them to last. Dryers use heat and heat destroys all types of fabric, but is especially brutal to natural fibers.