There are a limited number of ways to negotiate without saying "no" and when you say "no", people are liable to take you at your word. At which point a company is not "bad" when they say "Ok, good luck".
I only know of two ways to counter offer without quite saying no. First, you can ask for time for another offer with better terms -- "Can I have a bit of extra time? I applied at X and made the final round, but they won't make their decision until next Tuesday. I prefer you, but they are offering Y". This does not reject their offer or their timetable, but lets them know that more money would move you from possible to definite. Secondly, you can change the details, but in such a way as it is not just asking for more. More vacation time against lower hourly wage or better performance for a bonus. Basically offer something in return, while indicating that the given offer might be acceptable.
If your counter is just $offer+$extra, then, as I said, it is entirely reasonable for them to accept your rejection of their offer and go on to their next candidate.
Why wouldn't a company respond to a counter offer?
A comapny is likely to respond to a counter offer if they believe there is a mutually satisfactory resolution. Whether that is the original offer, or another counter offer, they must believe you will be happy with the result. If they believe you will be unhappy, even if you accept the offer, they are going to at least hesitant to offer the position to you -- you can always leave, and having you leave will be distuptive. Why take the risk that you will quit without even starting because you have a better offer (several questions on The Workplace revolve around that scenario). Even if they think you might be happy, your offer may change how they view you, making you a less desirable candidate.
Why do companies normally respond to counter-offers? Why negotiate at all?
Companies normally respond to counter offers because they can either agree to the offer, or there is some middle ground which they can agree to, which they believe you will be happy with. The reason they even entertain negotiation is because rejecting a offer doesn't get them what they want - someone to do the job. If they reject your offer and go to the next person on their list, they have no guarantee that person will accept their offer, and at least some evidence that they might (after all, you did). As they go down the list, they would be getting less desirable candidates and using extra resources to do so.
In short, as long as you aren't too far apart, it is probably easier to accede or reiterate the original offer, but it is not bad (for either side) to just let it go.