You can read on Wikipedia what four way handshake is. Basically, it's the way the client (PC or mobile) requests the ACK packet while it provides encryption password. For the problem with connection, I recommend switching the security protocol of your WiFi from TKIP + AES to AES only. This is known to increase compatibility with devices that don't support the TKIP + AES or TKIP connection mode. I have the same problems and I was able to fix them by switching from TKIP to AES.
