Not only is anymore a word, but you must use it and not "any more" in that context.
I'm not sure ... this English translation doesn't sound right to me. If we split up "any more" it would change the meaning to "more often", in my mind, which would actually make this sentence make a heck of a lot more sense to me.
"How come she wasn't coming anymore?" This is such mangled tortured English I wonder what it means. Does it read OK in Italian?
Perchè lei ha smesso venire is my attempt at "Why has she stopped coming?". The hints say
come mai means "how come". If so I guess one could say
Come mai lei ha smesso venire. The 'smesso' + infinitive for 'stopped' + present participle looks useful. But it is not the imperfect ....
I think it's right but since there is a 'non' in the sentence I think the answer should have one too if possible.
that's the official answer. I put how come she doesn't come anymore and it was wrong.
Maiden & Rombustelli have a long and pretty confusing discussion of how the Italian imperfect is used. They say (I think) the if the speaker does not specify the temporal bounds of the event - so when it began and/or ended are vague - then the imperfect is approptiate. So I think your answer is fine because it is completely vague as to temporal boundaries.
I begin to think that Italian tenses do not map very tidily onto Engliah ones. This means a lot of heart break.
I do not think the provided translation is correct English, or at least, I do not understand it. I had guessed the translation "how come she didn't come more often". It remains unclear to me whether "piu" here means "come more" as in "come more often/frequently" or something more akin to "anymore".
If it means something like "anymore", I can think of two possible meanings. One is that we are telling a story about the past, and she stopped coming some time in the past, but the "present moment" of this sentence is also in the past. E.g. " he said that she doesn't come anymore ". In this case, I might say "Why did stop coming?" or "why did she come no longer?".
In another case, we are referring to the fact that at some point in the past, she stopped coming, and this fact continues up until the present moment. In this case I might say "how come she doesn't come anymore?".
Also, there is apparently considerable variation in terms of how "anymore" is used across US dialects. I only use "anymore" synonymously with "no longer". Others seem to use it where I would use "nowadays" or "presently", and this usage always sounds strange to me. I don't mean to claim that my dialect is "more correct", just that whether or not this sentence makes any sense at all probably depends heavily on regional variations in the meaning of "anymore".