I've been having the same issue for days now with an integration that also just "used to work before".
Out of sheer depression, I just tried
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls | SecurityProtocolType.Ssl3;
This solved it for me..even though the integration strictly only makes use of SSLv3.
I came to the realization that something if off since Fiddler reported saying that there is an "empty TLS negotiation cipher" or something of the like.
Hopefully it works!