Apple Watch Series 3 Workout not adding to my Exercise ring! Why not?
Is your walk actually exercise?

Considering the intermittent nature of your issue, I’m wondering whether all your walks are actually exercise? 

According to the Health app on your iPhone:


  Every full minute of movement equal to or exceeding the intensity of
  a brisk walk counts towards your daily Exercise Minutes.


NOTE: Emphasis mine

So, if you’re just going for a casual walk it’s not likely to count towards this ring. If your walk happens to be at a faster pace, it will. This would explain the intermittent nature of your experience with the Exercise ring, and also explains why the Move ring still works, because even a casual walk will burn calories.