We have connected our domain to Cloudflare some weeks ago, using DNS proxy and other services (Pro plan). Since joining we are experiencing HTTPS Packet Loss / Lack of Service (1500ms max timeout) of 4% between Cloudflare and our servers. The packet loss is not constant, but appears in peaks randomly.
It definitely is not. This usually happens when the host rate limits IPs or it has some connectivity issues and, as all requests are now coming from a smaller set of IPs these issues can happen. You should probably talk to your host.