Christmas gifts are not performance bonuses. They are "hey, you are a human being, and so am I. Happy Holidays!" Allowing other, professional issues to bleed into that "other side" gesture implies something about the valued humanity of one side or the other, possibly.
If you have issues with performance, they should be handled through normal performance review channels, normal disciplinary channels, normal compensation increase/bonus channels.
If this person's professionalism bothers you enough that you dislike them and don't want to contribute to a gift from the people who avail themselves of her work throughout the year, according to company etiquette, then don't give. But I have to feel that being conspicuously absent from a gesture of holiday appreciation is not going to improve issues, at all. You're going to add very specific personal drama and resentment to the mix.
Whether you give gifts at work, in general, is only relevant if someone else works in a direct support position for you as an administrative assistant does. This is a common gesture, from those who make a lot more money and benefits, to those who they ask to do scut-work they'd much rather not do themselves. Not only do they make less, but their work tends to be much more of a drudge, specifically because they're doing your drudge-tasks so you don't have to. That's what the gesture acknowledges.