I have a program running from tomcat 8, postgresql database is used locally.

The program is doing some operations and ran flush several times successfully. But at a certain point in the program it just hangs:
em.flush();
where em is EntityManager and also debugger shows that its inside of the SocketOutputStream.socketWrite function never getting out of it.

How can I fix issue or find the reason?

It can be either because:

1. You have a bug in the JDC Driver
2. You submitted a huge load to the DB, so the Connection is stuck waiting for an answer

I guess the 2nd case might be true. Though not sure why. I'm debugging it and seeing that it has stuck on execution of insertion operations (there are around 3600 of them).
it worked well with first 1055 insertions and the next one stuck in the loop:
executeActions function of ActionQueue.

Is there any way to figure out why it is the case that it hangs there?

Why don't you just break it into multiple batches which clear the Session in between two batch executions and commit the transactions after N batches?