Welcome to AF!

Do you have 3G on in the background? On some handsets, if the phone thinks it can get a better connection to the net, it will cut off WiFi and use the 3G connection instead. try and make sure that when connected to WiFi, you turn of Mobile Network in Settings -> Wireless & Networks and see if that makes a difference.

Also, assigning yourself a static IP can make the connection a bit more stable, have you tried that? If you need instructions on that, let me know.

 

I'm not sure what else to suggest then, sorry.

Do you have any 3rd party apps installed which might potentially control connectivity? I'm thinking Juice Defender/Green Power etc?

 

It might be a software issue, I don't actually have the handset, I was just looking through the unanswered threads and stumbled across this. Generally the fixes I suggested work across a number of handsets.

Someone who owns the handset might be able to chime in before you take it back though.

 

As suggested by El Presidente this might be a software problem. I'd suggest to run the Repair Phone option on the PC Companion, this might solve the issue and if it doesn't then you know that you need to either bring the phone back to the store where you bought it to have it replaced or to a Sony Ericsson service center so it could be evaluated be a repair technician.