How frustrating! If you're having Wi-Fi issues with both of your iPads and if rebooting your router cures it (at least sometimes or for a time) it's most likely that it's a network issue and nothing to do with your iPads.
Having said that, here are some tips...
Several things often help improve WiFi connections on the iPad. Simply shutting down apps and restarting the iPad can fix most issues.
Quit Apps: To quit an app double press the Home button and the Multitasking Tray will appear at the bottom of the screen revealing all of the open apps. Tap and hold any app icon until all of the icons start jiggling. A red circle with a "-" (minus sign) will appear in the upper left-hand corner of each icon. Tap the red circle and the app will close.
If that doesn't do it, try restarting the iPad and if that still doesn't do it try resetting it.
Restart the iPad: Press and hold down the Home button on the front of the iPad for few seconds until the red slider appears, slide this across to shut the iPad down. Restart the iPad by pressing the power button on the top until the Apple logo appears.
Reset the iPad: You can do this by pressing the Home button and the Sleep/wake button on the top the iPad's case and holding them down together for at least 10 seconds, until you see the Apple logo. The iPad should then reset itself. The boot up process takes a few minutes and then the iPad should be responsive again. More here:
iPhone, iPad, iPod touch: Turning off and on (restarting) and resetting
Delete and Setup Wi-Fi: You can try deleting the network connection on your iPad and then go back and set it up again. Settings > Wi-Fi > tap on your network > Forget this Network.
Other tips...
Distance from the Wi-Fi router can impact the signal as well as interference from other electronics including microwaves, wireless home phones, cell phones, etc. Walls and floors with metallic studs can have a negative impact on Wi-Fi signals as well. Sometimes moving the Wi-Fi modem/router closer to where you use the iPad most can help.
Ensure that your router is running the latest firmware. Determine what version it's currently running and then visit the manufacturer's site to see if there's an update...follow the update instructions accordingly.
Another tip is to reboot your network and everything on it including your modem, router, etc. while your iPad is off. Turn your iPad back on and see if the connection has improved.
The iPad is optimized for the WPA or WPA2 security protocol. Setting the modem/router to WPA or WPA2 will often improve and stabilize Wi-Fi connections. If you have an older router that is only capable of WEP security it should probably be replaced...WEP is no longer secure and the iPad may have trouble connecting and staying connected.
Here's some more info if none of that works...
iPad: Issues connecting to Wi-Fi networks
http://www.ipadforums.net/ipad-help/30525-checklist-troubleshooting-wi-fi-connection-problems.html
iOS: Troubleshooting Wi-Fi networks and connections
http://www.ipadforums.net/ipad-2-forum/38535-slowing-i-pad2-2.html#post291682
Hope that helps!