Site down when Argo turned off

Our site has been running for a few months with Argo turned on. We were paying for that service, everything was running fine.
Today I turned Argo off. Exactly at that moment, our site became inaccessible, because of a cert error:

ERR_SSL_VERSION_OR_CIPHER_MISMATCH

The outage was reported by site24x7.com from our all testing locations:

|Location|Reason|Resolved IP|
|---|---|---|
|Milano|SSL/TLS Certificate Error|104.28.25.216|
|Istanbul|SSL/TLS Certificate Error|104.28.25.216|
|Sofia|SSL/TLS Certificate Error|104.28.24.216|
|Athens|SSL/TLS Certificate Error|104.28.25.216|

To bring our site back online, I had to switch cloudflare proxy off, send all traffic to our servers. Then, when clients got the new DNS, the traffic to our site gradually recovered, in about 10 minutes.

It this an expected behaviour? How can I prevent site outage when I want to switch Argo off?
We were paying quite a lot of money for Argo, but now, my trust in Cloudflare is shaken.

Vojtech