That is indeed not normal. When I had that in the past, I could (almost) always get adhesion again with repeated and very firm scrubbing.
On that one occasion where that still didn’t help, I thought about replacing the plate but was able to get it working again using some steel wool during cleaning. It can damage the coating but since I was about to chuck the plate, it was a worthwhile last ditch effort.
The type of dishwashing liquid could of course also be an issue. But I would expect issues to arise pretty quickly and suddenly after cleaning as the wrong type of liquid (scented and or oiled) would lead to a widespread, thin contaminant film.
Dawn or Palmolive are usually reported to be pretty good while I myself use a no-name brand.
It is also worth to double check your workflow and consider the materials printed. When using both PLA and PETG for example, cleaning is needed more frequently and more thoroughly than only single material plates.
For others, simply cleaning and trying to print on the other side has been useful. Due to my workflow however, I do not use gloves when handling the plate, I always leave fingerprints on the rear.
Finally, I keep my plate cleaning utensils (microfibre cloth, nail brush) in a dedicated place. There’s no telling what they are used for by other members of the household when I forget and leave them by the sink 
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Addendum: It is also worth noting that in particular the build plate should not come into direct contact with silica (beads, liquid). Either directly or dust transfered accidentally by hand. Silica is a very common cause of all kinds of adhesive failures, not only in FDM. Fortunately, the dust tends to wash away easily from the plate if not “baked in”.