End of day Friday update:
We here at CCP have tirelessly been keeping WOW! and Cloudflare updated on this issue all week and how it is impacting you, EVE Online players at WOW! Internet.
Current status is that we at CCP are in contact with multiple people at WOW! at all levels of the company, have an open support ticket with Cloudflares’ Enterprise Support, and we have been bridging communication between WOW! and Cloudflare. Both WOW! and Cloudflare confirmed this afternoon that they are now in direct contact, diagnosing and trying to resolve this issue, which is a network routing issue between WOW! and Cloudflare.
Please send both us and WOW! a support ticket with details.
EVE’s Customer Support confirmed today that the only pattern to these disconnect issues are customers of WOW! Internet. Some very few other players are also experiencing disconnects and we want to hear about your experience in a support ticket (see Are you experiencing issues staying connected to EVE Online? if you are not a WOW! customer) but those issues are more localised.
To WOW! customers then I want to mention that using a VPN will resolve your issue; it has been confirmed by multiple players. VPN-ing out of WOW!'s network to just about anywhere (towards London) means you avoid the network routes that are broken at the moment. See https://support.eveonline.com/hc/en-us/articles/203629415-VPN-and-Proxy-Use for details.
We here at CCP continue to work on this issue on your behalf.