They certainly will. Usually responsible disclosure is defined as some form of contacting the party involved, working out some window of time that you both agree on during which they can fix the bug (~30 days say), then disclosing details of the vulnerability. This is like a very polite and necessary threat.
If you care I would contact them again and let them know you plan to make the vulnerability public, and ask how much time they need to fix it.
It's persistent if it can be saved in a comment or on a profile, etc, and is much more dangerous if so. Non-persistent XSS realistically isn't too big a deal, most sites are vulnerable and it's usually only a problem if you're a big website and therefore vulnerable to phishing attacks.
Imagine if I could make you the author of this comment, it's like that.
I found an xss vulnerability in a website that can be used to cause noticeable problems (enough that fixing it should be a priority) so I contacted the developers behind the site and informed them what caused it, how to fix and an example of it in practice and why it's bad: they've done nothing in over a month. What do I do?
I guess the answer is "forget it", but I feel like if I don't do anything someone malicious will discover the issue and cause harm to users of the website...