This is not normal, but try to reset your MacBook's network connections as follows:
Go to (Apple menu) > System Preferences > Network. In the left column select Wi-Fi, then click the Advanced... button.
Under "Preferred Networks" select each network that appears and delete each one using the "–" (minus) button. Check "Remember networks this computer has joined" if it is not already checked.
OK then Apply. Quit System Preferences.
Under the Mac's Wi-Fi icon, select your network and supply its password.
If that does not fix the problem, your MBA may simply be defective. The best way to be sure your MacBook is working the way it should is to test it with a variety of other wireless networks, preferably in an Apple Store so that you could have a Genius diagnose it if necessary.