I'm using cipher suites which Mozilla recommends: https://wiki.mozilla.org/Security/Server_Side_TLS#Recommended_Ciphersuite
No problems in handshake simulation for all devices: https://www.ssllabs.com/ssltest/analyze.html?d=raymond.cc
On two different real Android 4.0.4 smartphones, I am unable to access my website with the error "Connection problem. A Network error occured."
I've also tested on BrowserStack, only Android 1.5, 1.6, 2.2, 2.3 works but 4.0, 4.1 and 4.2 don't work.
Server is running LiteSpeed 5.0 RC1 with OpenSSL 1.0.1e-fips 11 Feb 2013. Can't change/use different versions of OpenSSL because it's built-in.