I am not seeing any repeated logins. I think you may be reading the logs wrong. When it says "login" the program isn't going through the full login routine (submitting username:password) it will check the cookies first, if they are good, it will not drop out, this is the "login" routine.
But your action could be improved. Rather than perform a repeat every 20 minutes with a 20minute fluctuare which can reduce the repeat time even more), it makes no sense when you have low daily limits: 4
Why not just run the action once a day and let the action process the 4 items that way? Each action the program will test the login status, so that is being tested a lot unnecessarily by your action setup. Or repeat every 6 hours, so 4 times a day with a 1 max_items, to hit your 4 daily limits?