David, I can empathize there, I had a daphne ('Carol Mackie') suddenly up and die this last spring. It had started to leaf out (deciduous here), flowered a little and then croaked.
Keith, if there are no dogs around, what about tom cats, you have cats I think?
Did you apply much fertilizer close to the azalea? Too much fertilizer can kill and azaleas apparently need very little (although deficiencies would need to be addressed).
If that spot is wet, is that a new thing or has it always been? Has something recently impaired the drainage?