Why and when precisely, should a manager go to the base, listen to the workers , listen to their stories, their opinions and suggestions?

I don't want to say that it should happen frequently because most managers cannot do it !

However a manager must do it every time he/she discovers that:

1. Employees wrongly behaved and caused major issue.

2. A critical problem occured

3. Motivation is needed

This is always a tricky one, and it depends greatly on circumstances.  A good starting point is a couple of times a day - any more than that and it starts to take up too much time.  Different times each day, obviously.