Can I leave Smart Alarm permanently connected to the battery of my vehicle?

NO, mainly because the device would be easily intercepted by thieves who first look for then neutralize devices that are connected to the battery.

NOT ONLY. The sophisticated charging system guarantees the longest possible battery life as long as the charge discharge cycle is fully respected.

Should the device stay permanently connected it would always be kept in charging mode and the battery could deteriorate rapidly due to the fact that it would never discharge.