Cannot connect to friends using Game Center

Hi,

Me & my girlfriend both have a legitimate iPhone4 (no jailbreak or anything like that).We have iOS 4.3 installed.

We would like to play games against each other, using the Game Center.

So far we have tried 2 games - 'Fruit Ninja' & 'Yaniv', and in both cases when onetries to invite the other for a game - we get a message 'Can't Connect' after 2-3 seconds of 'Waiting...'.

We have tried dozens of times, in different times of the day, in different locations - using 3G or Wifi (both of us), and out of dozens of tries - we have managed to connect to each other only once on Wifi, and only once on 3G (the 3G time was interrupted

during the game).

The connection to the internet itself works fine, we can both log into the game center app and see our scores and each others scores in the different games, but we cannot seem to connect to each other.

This is not a problem with the game itself, because we have tried connecting with 2 differenet games.It's a problem with the game center.

We have made sure all notifications for the game center and the games themselves are turned on.

We have tried 'killing' the game center app and the game app itself, and trying from fresh - didn't work.

We tried logging off the game center and logging back on - didn't work.

We are frustrated that this simple task gives us so much headache.

Can someone please help us solve this problem ???

Thanks.