I have further update.
We have several environments and it turns out that while one of them exhibits the handshake problem, anther one doesn't.
The main difference between the two environments I tested was that the one where we see the problem is only accessible through VPN. However, I'm not sure if that is the real reason, there might be something else in play, maybe different setup of servers of those environments which I will investigate next week.
Also, I tried to issue simple requests for both environments directly from java, not through SoapUI and the result was the same.
Since both environments work fine when accessed through any browser, it looks like this is java SSL issue and not related to SoapUI at all.
I also found suggestions to use java 1.8.0_45 because in later versions certain older ciphers were disabled. That didn't help either.
Have you changed the java settings in soupui.bat?
...
set JAVA=%SOAPUI_HOME%..\jre\bin\java
...
