Am I right to assume that your covariate is expected to be associated with your grouping variable i.e. age (years) would be with *** on attractiveness
You would expect males and females would decline in attractivness as they grow older from age 18 to 65.... but there may not be any difference in attractiveness at age 18 between men and women, men become significantly more unattractive my age 25, whilst women remain only slightly less attractive as they did at age 18! But... by the age of 65 both men and women are as unattractive as eachother again!
(the effect of age on attractiveness is the same in men and women- however there is an iterraction as the interraction graph lines will not show the same response to age)
I had always thought that this sometimes happened, and although you may get a significant interraction its sometimes good idea to plot your interraction graph to see where the interraction lies.
Rather than using a covariate Try using your covariate as an additional factor? or multivariate regression?
Hope this helps?