Dogs enrolled in a previous study were assessed two years later for reliability of their local/global preference in a discrimination test with the same hierarchical stimuli used in the previous study (Experiment 1) and with a novel stimulus (Experiment 2). In Experiment 1, dogs easily re-learned to discriminate the positive stimulus; their individual global/local choices were stable compared to the previous study; and an overall clear global bias was found. In Experiment 2, dogs were slower in acquiring the initial discrimination task; the overall global bias disappeared; and, individually, dogs tended to make inverse choices compared to the original study. Spontaneous attention toward the test stimulus resembling the global features of the probe stimulus was the main factor affecting the likeliness of a global choice of our dogs, regardless of the type of experiment. However, attention to task-irrelevant elements increased at the expense of attention to the stimuli in the test phase of Experiment 2. Overall, the results suggest that the stability of global bias in dogs depends on the characteristics of the assessment contingencies, likely including the learning requirements of the tasks. Our results also clearly indicate that attention processes have a prominent role on dogs’ global bias, in agreement with previous findings in humans and other species.