No, the DoTs you put on a mob have no effect on whether or not root breaks.
What level are you and which giants are you trying to kill? In my experience, you want to be casting on mobs no more than 85% of your level. So, if you are level 24 trying to solo a level 23 giant, you're going to have a lot of root breaks.
Also, which DoT were you using? The swarm line has a -MR modifier which makes it easy to land on higher level mobs, compared to other spells. This may explain why your dots are landing but your roots keep breaking.
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