Well, maybe someone will prove me wrong, but physics was a subsidiary subject for my maths degree (and I've taught both Physics & General Science) and I can't think of any way that the very low levels of electromagnetic radiation that escape from a domestic microwave oven could deplete alkaline cells.
Thanks Buenchico, I am now suspecting an internal human culprit here who has probably mixed flat cells taken from those bl***y air-freshners that are all over our house!!