I bought my modem to work today and asked the IT guy to fix for me. 😀
We found this problem not only affecting my iPad 3, his iPhone and iPad 2 had the same issue with my modem, but the work's wifi or modem works perfectly fine with my iPad 3, so we know it's the issue of my modem.
He helped me to retore my modem to factory settings....and it's all fixed. 😁
Try it and see if it works for you guys.
Steps: Access your routers configuration screen (for most routers, open a browser and enter the address 192.168.1.1) and restore the settings to factory default. Re-entered user name and password for your internet access and re-set your wifi settings. Test your iPad 3 and see if it remembers the network upon reboot. 😍