いつも is "always". It can't be "this time". Not sure why this is confusing you - did you see a dictionary entry or other source that made you think otherwise?
I would treat it as a simple statement:
"But the girl is always alone."
Nothing is explicitly said bout how she "feels". (It is implicit from context in both the Japanese and English, of course). If it's a big house, she can easily be alone even if other people are in the house (e.g. parents fighting or in their separate rooms, not interacting with the child).