I run my small engines dry, never store them with gas in the tank. No issues doing that. No need for additives, premium fuel (?) or anything else.

What I found happening is that the gravity fed fuel bowls would slowly evaporate, leaving behind resin, then the float would open and the tank would fill the bowl and it'd start all over. Eventually the passages in the carb gum up solid and it no longer works. Sometimes you can hose them out with some carb cleaner, sometimes you can use an ultrasonic cleaner and sometimes you just have to buy a new carb.