Here's a list I've compiled of multiple solutions on how to fix the iPad's dropping WiFi. If your iPad can't access the internet at all then this is not the list for you. If your iPad shows incorrect password when it is in fact the right password then some solutions here may work for you.
1. Move closer to your router
2. Turn WiFi off then on again.
3. Restart you router.
4. Update your router
5. Update your iPad.
6. Renew your lease by tapping Settings > WiFi, pressing the arrow next to your network name (SSID) and clicking Renew Lease.
7. Forget your network then rejoin. Tap Settings , then select Wi-Fi. Choose the network with which you are experiencing difficulty, then select Forget this network. Go back to the previous screen and rejoin the network.
8. Reset your Network Settings by going to Settings > General > Reset > Reset Network Settings. You will need to rejoin to your network once completed.
9. If you know your IP addresses, DNS address, Router address and Subnet mask then go to Settings > WiFi then click the arrow on your network, click 'Static' and manually enter your addresses. Do not worry about the Search Domains.
10. If no. 6 does not work then try changing the DNS address to an OpenDNS address (208.67.220.220 and 208.67.222.222)
11. Oddly, lowering your brightness setting may work (making it higher may also work). Also turning off auto-brightness may work.
12. Set your channel (on your router) to 11. It this does not work then try Auto.
13. Set the HTTP Proxy to 'Auto' (Settings > WiFi > (select your name) > Select Auto). If this solution does not work then set it back to Off.
14. Switch your Security setting (on your router) to WPA2 or Mixed WPA & WPA2. (This solution worked for me!)
15. If you see something like a "Key Timer", "Group Key Timer", "Group Update Time Value" or "Group Key Update Timer" in your router security settings then set it to 0. If you see something like "ARP" then set that to 0.
16. Try everything at http://support.apple.com/kb/HT4199
17: Try creating separate network names for each separate bands network (i.e. add a G to the end of the name of the 802.11 b/g band, n to the 802.11 n band) and making sure both bands networks use the same security settings.
18. Try turning off Ask to Join Networks. To do so, tap Settings, then select Wi-Fi. Now slide Ask to Join Networks to off.
19. Turn off Bluetooth.
20. Try (in your router settings) changing the fragmentation threshold to 2048 and the CTS/RTS threshold to 512.
21. Try resetting your router (WARNING: You will have to reconfigure your router afterwards as it'll lose all its settings).
22. If all else fails, you may have to buy a new router.
Another thing you could try is putting your iPad into a DMZ.
This list will grow from time to time. If I've missed anything then please give me a heads up!
1. Move closer to your router
2. Turn WiFi off then on again.
3. Restart you router.
4. Update your router
5. Update your iPad.
6. Renew your lease by tapping Settings > WiFi, pressing the arrow next to your network name (SSID) and clicking Renew Lease.
7. Forget your network then rejoin. Tap Settings , then select Wi-Fi. Choose the network with which you are experiencing difficulty, then select Forget this network. Go back to the previous screen and rejoin the network.
8. Reset your Network Settings by going to Settings > General > Reset > Reset Network Settings. You will need to rejoin to your network once completed.
9. If you know your IP addresses, DNS address, Router address and Subnet mask then go to Settings > WiFi then click the arrow on your network, click 'Static' and manually enter your addresses. Do not worry about the Search Domains.
10. If no. 6 does not work then try changing the DNS address to an OpenDNS address (208.67.220.220 and 208.67.222.222)
11. Oddly, lowering your brightness setting may work (making it higher may also work). Also turning off auto-brightness may work.
12. Set your channel (on your router) to 11. It this does not work then try Auto.
13. Set the HTTP Proxy to 'Auto' (Settings > WiFi > (select your name) > Select Auto). If this solution does not work then set it back to Off.
14. Switch your Security setting (on your router) to WPA2 or Mixed WPA & WPA2. (This solution worked for me!)
15. If you see something like a "Key Timer", "Group Key Timer", "Group Update Time Value" or "Group Key Update Timer" in your router security settings then set it to 0. If you see something like "ARP" then set that to 0.
16. Try everything at http://support.apple.com/kb/HT4199
17: Try creating separate network names for each separate bands network (i.e. add a G to the end of the name of the 802.11 b/g band, n to the 802.11 n band) and making sure both bands networks use the same security settings.
18. Try turning off Ask to Join Networks. To do so, tap Settings, then select Wi-Fi. Now slide Ask to Join Networks to off.
19. Turn off Bluetooth.
20. Try (in your router settings) changing the fragmentation threshold to 2048 and the CTS/RTS threshold to 512.
21. Try resetting your router (WARNING: You will have to reconfigure your router afterwards as it'll lose all its settings).
22. If all else fails, you may have to buy a new router.
Another thing you could try is putting your iPad into a DMZ.
This list will grow from time to time. If I've missed anything then please give me a heads up!