When serving patrons in the Den, just bringing them what they ask for initially is not enough...
You need to keep attending them. Even if you or the slave who was serving them before has been dismissed, keep checking back.
Watch cups and dishes to see if they have become empty or are not being touched.
If a dish or cup is empty, ask if you can refill their drink or bring them any more food.
If what they were eating is very messy or greasy, bring a warm, damp towel and offer it to them or offer to clean their hands/face for them.
If they wish you to clean them, do so reverently, as though you performing the service for a god or goddess, not the way you would wipe down a small child!!
Remember, you are a slave, existing for the pleasure and convenience of the free.
Pay attention to body language.. If someone is looking around as though they are trying to find something, even if they have already been served what they asked for, go ask if you may bring them something or serve them in any way.
If someone's plate or cup is empty, but they are busy, perhaps in conversation with another, you must make your inquires very subtle, so as not to interrupt.
Rather than kneeling right in front of them, at their feet, kneel to the left of them (or to the right if there is no space or they are left handed) a pace or so back and look attentive. Once you catch their eye, a simple glance and head gesture at the empty cup or dish can be used to see if they desire something or wish their table cleared. Again, your goal is to be pleasing.