My iPad 2 also occurs the plight of one minute dropped once, with a variety of search methods, and costs a lot of time setting up the router, all not fix the issue, which includes, iPad 2 WiFi signal strength weakly, unstable, connection speed been changed and so on. Following describes I explore the fixes for you, only for reference.
First you need to set the iPad 2
1. Restore network settings
Settings – General – restore network settings, then restart the iPad 2 (while holding the power button and home button 7 seconds), preferably also restart the router.
2. Turn off some Push features and Notification, such as Push, FaceTime, Find iPhone, Notifications and other features.
Use a static IP address
Settings-WIFI-click “>” on the right of the wireless network, then click the static and fill in the IP address, subnet mask, router IP and DNS.
This recommended Google’s DNS, setting the DNS to 126.96.36.199,188.8.131.52
5. Electromagnetic compatibility issue
Try removing the smart cover
6. Power off
Some suggested to reset the network settings on your Ipad (see above) and switch off the router for 60 seconds as well.
Followed by the router settings
1. Upgrading the router to the latest firmware.
Some routers may be dual-band (2.4G and 5GHz), the best to use a single frequency. If you have two bands 20Hz and 40Hz, preferably 20Hz.
Some routers have this Settings, then change it (open changes to off, or off changes to open) try it. Some people say that useful.
Change WEP into WPA2.
These are few reasons found to lead the issue of iPad 2 WiFi connection, If I find other possibilities I will add them here.