How do I solve problems with connecting to some mail servers from a VPS?

One of the possible reasons for this problem is that many firewalls refuse connections from servers with enabled TCP ECN (Explicit Congestion Notification). To access a site behind such a firewall you will need to disable ECN on the hardware node by running:

sysctl -w net.ipv4.tcp_ecn=0

and adding the following line into /etc/sysctl.conf:

net.ipv4.tcp_ecn = 0