Shopify itself is very reliable. The parts you own, the custom domain, DNS, apps and theme code, are where problems start.
Monitor the storefront with a keyword
Check the homepage and a top product page for a phrase like Add to cart. A broken theme or app can return 200 with an empty page.
Monitor DNS and SSL
Your custom domain's A and CNAME records and the certificate expiry are the usual culprits after a domain or DNS change.
Watch response time
Apps that inject scripts slow the store down. A response-time threshold shows you when a new app made things worse.
Tell customers
A status page on status.yourshop.com answers is it down before customers email you.