If your current web host only provide shared IP for your websites, there are chances that you are experiencing IP blocking which is controlling by your ISP.
IP blocking prevents the connection between a server/website and certain IP addresses or ranges of addresses. IP blocking effectively bans undesired connections from those computers to a website, mail server, or other Internet server. If one of the website is having problem on your web host's server, your ISP might blocked it to avoid problems. Therefore, all other websites under the same web server will also be blocked since they are sharing with the same IP address.
Here is an article that showing the importances of an unique IP in term of web hosting.
https://kb.doteasy.com/questions/496/Why+do+I+need+a+unique+IP+Address%3FFYI, unique IP addresses are offered on both our Ultra Hosting and Unlimited Hosting plans at NO additional cost. Feel free to let us know if you are interested to transfer your hosting service to Doteasy and we will more than happy to assist you further.