The number 1365 is limited by the open files, 4096 in ulimit ( 3 X 1365 = 4095) . To avoid the connectivity issue itself you can increase the open files by modifying the etc/security/limits.conf in Linux. If you find it is there already then consider to add it to splunk start up script
i) initd script, add the below and change the start/restart to call the function
ii) Under systemd you can increase it using LimitNOFILE
But 1300+ HEC connections are very high you may want to monitor the performance over the network, like netstat -an will show if the TCP Recv queue is building up or not. Then you may need to load balance the # of connections by spawning another HEC receiver.