Java 1.8.0_140 and below will return a handshake failure for any browser that doesn't support SNI: https://stackoverflow.com/questions/36323704/sni-client-side-mystery-using-java8
Turns out this is a JVM bug: https://bugs.openjdk.java.net/browse/JDK-8144566
That bug was fixed in: http://www.oracle.com/technetwork/java/javase/8u141-relnotes-3720385.html

Please update the JDK for the Jira Enterprise Release to 1.8.0_141 or above.