We received a feedback from m**@in*.lv:
If Check Point Software Technologies firewall used, then in Inspect or Bypass used for HTTPS, then FIRST connection to specified https site fails. Second-third... and so on connections works OK, if they go to the SAME IP address. If IP changed for specified host - first SSL connection fails again, and so on. Because all addresses in Amazon Cloud are Cloud Addresses, it's impossible to avoid this problem.