ZZR's did suffer from carb icing. mainly the bigger ones. it was the vacuum created from the fairings sucking the heat away from the carbs.
being water cooled you could tap off a small hose and run around the carbs to keep them warm if there isnt water circuit allready round the carbs.
but as I said I would think it would die until they heared up again. which is [possibly not icing that you have.
check terminals, may even be a loose battery terminal or battery going down.
ZZR also known as ZX
another possibility,dirty fuel or water in the fuel .
doubt it would be diaphragms as would happen more often, but could allways be if neer changed.
