Establishing an SSL session is a resource intensive process, you might want to check whether your server is overloaded, it might me the case it lacks resources like CPU, RAM, etc. when you put the load onto it hence it fails to respond to the handshake in a timely fashion.
You could consider using i.e. JMeter PerfMon Plugin to ensure that the server (and JMeter as well) have enough headroom to operate in terms of CPU, RAM, Disk, Network, etc. cause it might cause the problem
If the server/JMeter is/are not overloaded but you still experience the issue you can temporary enable debugging of SSL events by adding the next line to system.properties file (lives in "bin" folder of your JMeter installation)
JMeter restart will be required to pick the property up, once you restart JMeter and run your test you should see a lot of SSL-related information in the stdout.
More information: Java Secure Socket Extension (JSSE) Reference Guide