Like last night, I couldn't sleep. This time, however, what kept me awake wasn't the neighbor, but the neighbor's dog.
It sounds a bit off without "however", but maybe it's just me? Why should I include it? Or why not?
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
You should include it. Strictly speaking, there's nothing wrong with omitting it, but the second sentence is drawing a contrast between last night and tonight. The "however" is what sets it up as a contrast. An alternative would be to use "but":
But this time what kept me awake ...
(Some may argue that you shouldn't begin a sentence with "but", and sometimes they'd be right. But in this case, just ignore them.)