If you are having issues connecting your device to a wireless network, your device may have been operating continuously for too long, and you will have to restart the device. Restart the device by holding down the power button and selecting to turn off. If you do not see the option to turn your device off on your screen, hold down the power button on your tablet for 40 seconds until it turns off, then start it up again.
If rebooting the device doesn't solve your problem, your tablet may be running outdated system software. Instructions on how to update your device software can be found here.
If you are still having issues, your WiFi connection may be the problem. When attempting to fix your WiFi network you should take these several steps (no particular order is required) :
Power cycling your wireless router. Instructions can be found here.
Changing the type of security on your router from WEP to WPA2.
Changing the setting on your router to disable 802.11n and limit it to 802.11g.
Finally, Changing the settings on your fire tablet to limit its wireless speed to 54Mb/second.