So I will now add to this thread. I have had my gs4 for about 3 weeks now and NO issues at all connecting to my wifi at home during this time. All of the sudden today I tried to do a group text and send a picture out. For some reason the text kept failing. I then tried to send a picture I had recently sent out to my mom about 5 days ago and send that same one to my wife and it would not send the picture over text. So after coming on this thread and seeing wifi issues I decided to turn off my wifi and try to send my wife the same picture and it went through. I then tried to resend that group text with a picture and it sent. Not sure why turning wifi off for this worked. I am also using the stock messaging app with the phone as handcent could never turn off the stock app correctly.
I wonder if it could be that I have my phone set to auto install apps from google play on wifi.