What model of AirPort Extreme do you have?
Is this the current "tower" shaped version......or......an older "flat or square" version of the AirPort Extreme?
IF.....you have the older "flat or square" version of the Extreme, the symptoms that you are describing indicate a power supply problem either with the outboard power supply "brick".....or...... the internal power supply components inside the AirPort Extreme.
It might be a $20 gamble.....unless you have a money back guarantee.....to try a new outboard power supply for the AirPort Extreme to see if that will solve the issue.
http://www.ebay.com/itm/ORIGINAL-OEM-APPLE-AIRPORT-EXTREME-BASE-STATION-POWER-SU PPLY-AC-ADAPTER-A1202-/370810566512
If a new outboard power supply will not work, then the AirPort Extreme has failed, and will need to be replaced.
IF.....you have the current "tower" shaped AirPort Extreme, a power supply component has failed and the AirPort Extreme will need to be replaced. The warranty is one year on the Extreme, but if you have AppleCare in effect on one of your Macs, the AirPort Extreme is covered up to three years from its purchase date.