I ve spent nearly 3 hours today and 4 hours last week trying to resolve this on my new S3. I was pretty flummoxed when the wifi signal seemed to drop off without any reason.
After much hunting, my initial hunch seems to be correct
a) Interference from other devices
b) Unable to get an IP address
c) I am just a layman when it comes to networking, but since all of my other devices at home the iPad, iPhone and my laptop seem to have no issues (my laptop occassionally has the same drop-off problem), I thought it's likely to be a phone issue rather than a router issue.
To resolve this I found another thread on the forum and I tried this, and Bingo! it worked.
Press these menu options on your phone: Settings > Wi-fi> (Choose your network by tapping on it for a few seconds) > Modify network config
Check "Show advanced options"
Choose IP Settings: "Static"
Enter these details
IP - 192.168.1.253 or 195.168.1.253
Gateway - 195.168.1.1 (I chose 192.168.1.1 since that's my router address)
NPL - 24
Netmask - 255.255.255.0 (I could not find this option)
DNS 1 - 8.8.4.4 or 8.8.8.8 (I had the latter by default and let it stay)
DNS 2 - 4.4.4.4
And save.
Presto! It just connected in a few milliseconds.
It may not be so simple for each phone, but it's certainly worthwhile to try.
Here is the link the forum thread, where I resolved it:
http://androidforums.com/samsung-galaxy-s3/610480-obtaining-ip-address-problem.html
Good luck