In Act I scene 1, when Lear sets up this very strange competition where his daughters are able to bid for their inheritance by flattering him, Lear also describes how he is going to conduct himself now that he has bestowed all of his possessions and land on his daughters:
Ourself by monthly course,
With reservation of an hundred knights
By you to be sustained, shall our abode
Make with you by due turn. Only we shall retain
The name and all th'addition to a king.
Lear seems to want to keep all the good parts of being a king without any of the responsibility, and this is demonstrated through his desire to be "sustained" with his one hundred knights by his daughters. Spending a month with one daughter before moving on to the next seems to further reinforce his inability to let go of his position completely, as that would enable him to keep an eye on how his daughters are using the power they have received from him. In short, this decision of Lear shows the audience a lot about what kind of a man he is: he wants all the trappings of power without any of the responsibility.