If you are jabbing or feinting every second, the feints become lose effect, the jabs lose power and become predictable you do not want to become predictable because you will make for a easy counter.

You do not need to be doing something every few seconds.

There is also drawing, which is lowering/dropping your hand, to invite opponent to hit you.
While very useful, is again something you do not want to be doing regularly as, the opponent will anticipate this and knock you on your ass.

Don't feel pressured to always be doing something with your left hand, becoming predictable is much worse than being inactive.

While you may see pro fighters do this in a single round they would not dream of doing it for every single round.

You want to be unpredictable, concentrating on moving your lead arm is distracting and the opposite of landing punches on your opponent.