I think as the comparisons between Henry VIII and Robert Baratheon were there for all to see, it's not a massive stretch to see the "Anne Boleyn" moment where Cersei is either removed by the High Septon, as stated above, or Robert does what she later did to Margery and line up some false witnesses who say that she slept with someone other than the King. A treasonable act which would have cost her life.
Either way, she was perfectly within her rights to be wary of such a fate. Arguably, the only reason Robert didn't attempt it after many years of unhappy marriage was that a) she was still hot and b) fear of what Lord Tywin would do in response. He was still his most powerful and richest vassal. The Kingdom was probably heavily in debt to House Lannister along with the Iron Bank so any withdrawal of credit could have been disasterous.