Give it a try please. I fixed this problem by disabling those things (dont know which one helped)
I was having "no error game quits" (Almost every game)
All animations was stoping ingame including on minimap, i can move at this short period, after 5-10 secs, it goes to black screen with a flashing cursor on top right corner, and game quits without errors.
Origin application settings > General >
Disable : Cloud Storage
Disable : Automaticly keep my games uptodate (make sure enable this when there is a patch)
Origin application settings > Notifications >
Disable all notifications
Origin application settings > Origin ingame >
Disable origin ingame
Origin application settings > Advanced >
Origin crash reporting : Never Send
Origin experience reporting : untick both options.
I am assuming you done fix all your Punkbuster problems , if not pls check here also > http://answers.ea.com/t5/Battlefield-4/constantly-kicked-from-every-server-by-punk-buster/m-p/1801661#M39675
Also check firewall settings, make sure PB, BF4 (edit: also ESN Sonar) files correctly configured for both Public and Private. In my case , i had multiple BF4 and PB firewall enteries and mostly they were either only Public or only Private choosed. So choose both private and public for all bf4 and pb enteries there. Or you can try this http://www.youtube.com/watch?v=qh7ayrsynr0
And both on firewall and router open ports :
TCP 80, 443, 9988, 20000-20100, 22990, 17502, 42127
UDP 3659, 14000-14016, 22990-23006, 25200-25300
