Check your server IP bindings, and/or disable Ipv6. I've had very similar symptoms over the last few days, and it turns out a hardware firewall that was blocking ipv6 traffic was replaced with one that permitted IPv6 earlier in the week, but the ISP wasn't forwarding v6. OBS was trying to connect to FB Live's IPv6 address and was failing.
In settings | advanced...check "Network" at the bottom of the window and ensure that "Bind to IP" has the IPv4 address selected instead of "default"... unless you canor want to disable ipv6 altogether.
May not work for you, but after hours of research, I thought I'd post the fix that worked for us.
ciao..
jr.