Living in Florida, we get a lot of rain that does a good job of keeping our solar panels mostly clean. To see if extra scrubbing was needed, I cleaned 1/2 of my solar panels after they had been installed for 11 months using a scrubbing brush and dish detergent.
The panels that I cleaned went up in power production by an average of 0.11 kWh/month. [0.11 kWh * 36 panels * 12 months = 47.52 kWh of extra power over an entire year…assuming the cleaning effect persists after the first month.] So this is a very small amount of power (about $6 worth at 13 cents per kWh.) in return for an hour of scrubbing. [And this assumes that the cleaning benefit lasts for a full year, which may not be the case.]
I would suggest only scrubbing your (Florida) panels every few years unless you notice a drop in performance.
You can download my data and simplistic analysis in the attached open document spreadsheet: SolarPanelCleaningExperiment