I have the same problem. After contacting my ISP and doing some troubleshooting their hosting provider seems to be blacklisting a bit to many IP's.
With another customer, we've tracked the problem to his ISP DNS.
Please try to set your DNS to Google's DNA:
Primary: 8.8.8.8
Alternate: 8.8.4.4
Indeed, we're using Shopify e-commerce platform.
That user was me
It's not the DNS. Indeed changing the DNS did help, but after this I contacted my ISP. They use exactly the same DNS, and had no problem whatsoever. When I do a traceroute I can reach every hop, except for the last one. So, probably I am getting blocked, and it isn't a DNS problem. Also at the moments the website does not work, I can still ping it, which resolves to the correct IP.
But it is getting better, the site is working quite often for me now.