In short yes, do not use Cloudflare :-D. Or make it work. :-D Today I was solving similar issue, when you proxy something (not CF,…) I put in the end of tunnel extra firewall. That sometime break this tunnel, because state of the firewall. I resolved it by increasing keep alive parameter on targeted server and enforcing proxy to keep alive whit lower TTL than targeted server, so tunnel is periodically “ping” from proxy even when no one is using it. If this is your case, I do not know, if you are able to tweak CF, I do not know, sorry,… Writing just bc of similarity of our problems 👍️
PS: Im talking only about https trafic, CF in lower tiers does not support proxy for smtp traffic,..