I just had this problem on my GT-i9305 Galaxy S3 (same for i9300 I'm guessing) where my SIM card kept ejecting itself. I hadn't used the phone for a while and was putting a new SIM in there and it didn't want to play ball - just kept popping itself out.
I fiddled for ages but what eventually fixed it was grabbing my air compressor and blasting the crap out of the slot. There must have been something under the spring clip and wasn't letting it fully depress. After that my SIM card slot worked as fun and didn't pop out.
Just thought I'd throw a thread up for reference as I couldn't find much on Google about this.