Many classes have a dot they can apply which they can refresh indefinitely through a second spell.
Blizzard remembers any damage modifiers (not spell or attack power modifiers) on the player at the time as well as the crit chance. This means you want to recast the buff if your crit or damage modifier (from tricks of the trade or various 2/4 piece bonuses) increases.
This mod will display the targets you have dots on, what damage modifier you were using at the time the spell was applied, and if you should reapply the buff or not.

