I have two groups of subjects, both undergoing two experimental conditions, and data are collected at three time points. I am interested in the time*cond and the time*cond*group interactions. When I don't include the group*time interaction, the three-way interaction is significant. However, when the non-interesting group*time interaction is included in the model, the three-way interaction is no longer significant.

Why does this happen and which analysis is correct?