Can you sue someone if their website says that they will email you back, but they never do?

Answer 1

No, because unless money or mutual promises are involved, enough to make a binding contract, a promise to send back an email is not enforceable. Unless you relied on that promise, to do something more than normal, to your detriment, there's no contractual obligation. Like saying to a friend you'll call them next week-- if you don't, maybe that's impolite, but it's not legally actionable.

But, you haven't even said what the website is, or what kind of email you were promised, etc., so with insufficient facts, you aren't going to get great answers.

Answer 2

What loss did you sustain by them not doing so?

Answer 3

No.