This behavior is normal for an ambient_generic. There is a flag called Is NOT Looped or Not Toggled, that determines what happens when it is triggered. If this flag is UNchecked, then behavior is set for a continuous looping sound, so first trigger turns it on, second trigger turns it off. If the flag is CHECKED, then behavior is set for a NON looping sound, so that each trigger plays the sound once. So if you have a non-looping sound, and you don't check the flag, the first trigger plays the sound, but after the sound is finished, the ambient_generic is still in the ON state, even though nothing is playing. The next time it is triggered, the ambient_generic turns off.
To rephrase: the on/off state of the ambient_generic is maintained separately, regardless of whether a sound is playing or not, and each trigger either toggles it on or toggles it off, like a light switch. The Is NOT Looped / Not Toggled flag causes the ambient_generic to switch on and then off again each time it is triggered, like a momentary push button.