What is the difference between saying:
Are you still working there?
Do you still work there?
Which is more common in spoken vs written English?
Google books returned results for both of them.
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There is a subtle difference. To my ear "Are you still working there?" is the more aggressive and challenging form, as in "Jeez, why are you staying at that crappy job?"
"Do you still work there?" sounds more neutral, as in "Hey, I haven't seen you since I left company x. Do you still hang out with those people?"
That might be because ARE YOU can be an auxiliary verb, which helps puts focus on the person addressed. DO YOU relies on a verb and the energy of the sentence is directed away from the person addressed, which I think sounds more polite.
For your specific example, "Are you still working there?" versus "Do you still work there?", when referring to having a job at a company both are commonly used, both are acceptable, and anyone who complains about one being wrong would be considered overly critical. Technically, "Do you still work there?" is preferable both in writing and in speaking.
However, if the situation is two people in a workshop, with "there" referring to a workbench, they have different meanings and you need to use the correct one.
"Are you still working there?" asks if you are currently using the workbench. Assuming two people cannot use the workbench at the same time, I ask "Are you still working there?" because if you are, then I cannot use the workbench, but if you are not, then I can use the workbench. I would ask this question if I could not tell whether or not you were using the workbench, for example because you were standing next to the workbench and talking on the phone. I'm asking "May I work there or do you want me not to work there so you can resume working there when you get off the phone?"
If I can see that you are working at the workbench when I ask the question "Are you still working there?" the question can have yet another meaning, similar to "Haven't you finished working there yet?" This choice of meaning is indicated by giving emphasis to the word "still" (by stressing the word when speaking or by using italics when writing). I'm expressing a belief that you are working there and surprise that you have not finished working there yet, and also asking for confirmation that you are still working there, and perhaps asking for an explanation of why you have not finished yet or when you expect to be done. In this situation, asking "Do you still work there" is wrong and I will sound like an idiot (or at least someone who does not know English well) if I ask it.
"Do you still work there?" is a question I would ask when you are not using the workbench. It means, roughly, "I know you worked there in the past; do you plan on working there in the future?" This is different than "Do you work there?" because "Do you work there?" implies that I do not know that you have worked there before. If the person I'm asking thinks that I should know they have worked there in the past and I ask "Do you work there?", my question will be confusing to them and will likely be interpreted as an incorrect way to ask "Are you working there now?"