hi,

maybe others will reflect as well, but my simple explanation would be that as follows: the significance is decided based on the residual variance, effect size and sample size, roughly. If time is a covariante then a part of the variation is attributed to the time variable, so the residual variation is less and you might be able to see the effect of the score. If you take out the time variable then the variance explained by time is now increasing the residual variation - and the increased residual variation might be too large to make the effect of score visible.

regards