I don't know definitively, but here are a few observations.
The mass of a planet is probably more important than the size of it (although both will be significant).
What gases make up the atmosphere? Earth's gravity is insufficient to hold on to hydrogen and helium, the two most abundant elements in the universe. On the other hand, carbon dioxide and methane are no problem.
The atmosphere on earth is remarkably thin. If you reduced the size of the earth to a 30cm diameter sphere, then two coats of reasonably thick paint would cover 98% of the space taken up by the atmosphere. So -- there isn't much atmosphere anyway.
Mars - away from our orbit (although, in astronomic terms, not by much) lost most of its atmosphere in the past, and part of the reason is that its gravity is only about a third of the Earth's - but it still has some atmosphere.
Not an answer, sorry, but food for thought?
