My SO and I have been discussing this for
years and everyone we've spoken with about this stared at us like we were crazy. It's weird finally encountering someone who is describing it in the exact same terms.
We do experience it in relation to our dishwasher sometimes, but I don't think the dishwasher is an essential component: it happens with handwashed dishes too. The essential factor, as far as we've been able to determine, is wet dishes which get in contact with outdoor air. However it only happens on some days and more often in some months/seasons!
My theory so far has been that it's a reaction between some molecule in air (something which varies in concentration over a period of days, perhaps a pollutant) and water. But it may as well be that it is interacting with detergent residue.
The interesting thing is that we don't actually manually measure detergent for our dishwasher but use detergent tablets, so the quantity never varies.