In this article I will talk about that I know a way to fix the problem of authentication and connect the same to the Internet, to distribute your Wi-Fi router, as well as what may be caused by such behavior.
Saved, protection WPA / WPA2 on Android
Typically, the process of connecting himself with the authentication error occurs is as follows: you select your wireless network, enter a password on it, then you can see the change in status: Connection - Authentication - Saved, WPA2 or WPA protection. If you later change the status to "Authentication failed" in this very connection to the network does not, then something is wrong with the password or security settings on the router. If you just write "Saved" it is probably the case in the parameters of Wi-Fi network. Now, in order that in such a case can be made to connect to the network.
Important note: If you change the wireless network settings on the router, remove the saved network on your phone or tablet. For this purpose, Wi-Fi settings, select your network, and hold it until a menu appears. In this menu, there is also the option "Change", but for some reason, even in the latest version of Android after the change (for example, the new password), it's still an authentication error occurs while after the removal of the network's all right.
Very often, this error is caused by an incorrect password is input, the user can be sure that all the inputs correctly. First of all, make sure that the password on the Wi-Fi do not use the Cyrillic alphabet, and when you enter you observe the case of letters (large and small). For ease of testing can temporarily change the password on the router to fully digital, how to do it, you can read the instructions for setting up the router (there is information for all common makes and models) on my site (and there you will find how to go in the router settings for the changes described below).
The second popular option, especially for older and low-priced phones and tablets - unsupported mode Wi-Fi network. Should try to include 802.11 b / g mode (instead of n or Auto) and try to connect again. Also, in rare cases, it helps to change the wireless network in the region to the United States (or Russia, if you have a particular region).
The following is to check and try to change - the authentication method and WPA encryption (also in the settings of the wireless network of the router, items can be called otherwise). If you have a default WPA2-Personal, try to deliver WPA. Encryption - AES.
If the Wi-Fi authentication error on Android is accompanied by a weak signal reception, try to select a free channel for a wireless network. Unlikely, but can help and change the width of the channel for 20 MHz.
Update: In the comments, Kirill described this method (which for reviews then many have worked, and therefore I get here): We go to the settings, press the button more - the modem mode - setting the access point and pairing. We put on IPv4 and IPv6 - BT-modem off / On (Leave to Off) Turn on the access point after turning off. (Upper switch). Also go to the VPN tab to put a password, after removed in the settings. The last stage is to enable / disable the flight mode. After all this, my Wi-Fi came to life and automatically connected without clicks.
Another way proposed in the comments - Try setting the Wi-Fi network password consisting only of numbers, can help.
And the last way, which in the case of which you can try is an automatic correction of problems using the Android application WiFi Fixer (you can download for free on Google Play). The application automatically corrects many errors related to a wireless connection and, judging by the reviews, works (although I do not quite understand how it is).