Some runners assume that they must work toward the day when they don't have to take any walk breaks at all. This is up to the individual but is not recommended. Remember that you decide what ratio of run-walk-run to use. There is no rule that requires you to hold to any ratio on a given day. As you adjust the run-walk according to how you feel, you gain control over your fatigue.
I've run for about 50 years, and I enjoy running more than ever because of walk breaks. During and after almost every run, I am energized and mentally alert. I would not be able to run almost every day if I didn't insert the walk breaks early and often. I start most runs taking a short walk break every minute. By 2 miles, I am usually walking every 3-5 minutes. By 5 miles, the ratio often goes to every 7-10 minutes. But there are days every year when I stay at 3 minutes and even a few days at 1 minute.
The run-walk-run ratio that you use will vary from day to day. The more conservative you are, the more enjoyment you can expect from your running, day after day.