Sorry for the necrothread, just thought I'd point out this is still happening.
I keep the fat indoors with the food and near the kitchen, so the fat and tallow can be used quickly for cooking. I've tried storing the fat in barrels with the rest of the food stockpile, or making a fat-only stockpile with no barrels allowed, so the fat is simply set down on the floor.
Randomly the job is interrupted, requiring that I go and requeue the task. Since its not really a task that can be done via the work orders screen, its one of those tasks that needs constant babysitting and not for lack of resources, but rather because the task is randomly canceled for no apparent reason.
The fat is just sitting there, either stored in barrels or directly on the stockpile floor in a food zone that accepts fat and only fat, and yet the task is randomly canceled due to a destroyed or missing item.
One thing I have noticed, though it may just be coincidence, is that fat laying on the floor without barrels is interrupted less often than when its in barrels. It could be something barrel related, but then it still gets interrupted when barrels aren't in the picture at all.
One suggestion I'd have would be to make render fat be an automatic task, like collecting webs. While the job could still be interrupted, at least it would restart on its own without the kitchen having to be babysat.