I have over 50 hours on my 705 HRM, and it's still the original battery. Maybe your HRM is defective, and doesn't shut off.
Most straps use CR2032 coin batteries. It's a lot cheaper to buy them online. I've used
Battery Bob: $13.75 for 11 Maxell batteries (1.25 each) , or $6.89 for 5, and free shipping.