If a non-flashing base starts flashing, you get the alert. As long as it continues to flash, you will not get another alert from that base. If it stops flashing, then starts again, you get an alert.
Typically, there are only a handful of bases that seem to attract action, and that action can last quite a while. So, while these bases are continuously flashing, you only get alerts from the other few bases that flash every now and then.
There is no magic or other parameters. When an enemy gets within the arena-specific trigger distance (and that distance can vary for bombers, fighters and vehicles) from a non-flashing base, the alert is triggered.