It's fine to leave it on 24/7.
Yes, pool automation systems are designed for continuous operation. The controllers, pumps, and relays are built to run constantly, just like your refrigerator or internet router.
The bigger risk is turning them off and on repeatedly, which stresses electronics more than steady power. That said, a good surge protector is cheap insurance. Lightning strikes and power blips are what actually kill these things, not continuous runtime.
One thing: if your system has a fan or vents, keep them clean and unobstructed. Dust and heat buildup are the real enemies of electronics that run 24/7. But the automation itself? Leave it on.