Eliana,
I think that is a linksys -cisco AP...
Usually linksys knows more about those units..
Cisco supports Aironet devices however I can tell you that it sounds like the usual behavior of linksys ...
Sometimes it works, sometimes it just stop working. So I would suggest you to make sure of power soure.
Try using a UPS for one of the units and see if it shows up the same behavior.
Some units are quite sensitive to voltage so if at some point the voltage varies the unit could get stock and the power cycle just make it work.
Make sure that unit is not overheating, or maybe is located in a non adecuate place.