If there is some level of engagement, and they haven't responded in a bit, I will send a follow up email after a bit. For example, I once negotiated back and forth with one potential buyer, and negotiations went south when I used the approach that a psychologist friend of mine had goodnaturedly suggested as the "I know how to sell this guy" correct way to deal with him.
Well, this psychological approach backfired and made the potential buyer, who was more of a straight shooter, back off and pretty much drop out of the negotiations. My mistake for trying something new - I am an excellent negotiator and know how to deal with people. But, the psych meant well and I guess he thinks that using a "story" and manipulation to try to make a sale is the way to go. I disagree.
Anyway, long story short - I waited two full business days and emailed the guy with a simple, "What did you decide to do?" , being careful to respond to a PRIOR email of his, so that the verbiage the psych had suggested I write was not contained in the email history, and sure enough within an hour I got a response. Within a few more emails I was able to close to deal at a price higher than what he had said he would never pay, but a little lower than what I had initially wanted. We both gave up some ground.
The point being, that if you have some emails back and forth and you experience radio silence, it is perfectly acceptable to email again to try to resume the negotiations, and in some cases, you will be able to revive a deal and make it happen.
BUT, if all they did is make a lowball offer, and you came back with a counter and they did not even respond - just ONE email from each side, I would leave it alone and move on. Unless you are willing to come down to very close to their offer, clearly they don't want to pay anywhere near what you countered or at least they would have responded.
In short - rule of thumb, hounding them if you are hopelessly apart in price, and you have not heard back from them, is not going to get you anywhere. Also, hounding them if all they did is make one single email, and did not even respond to your counter, is probably not going to result in any deal either.
I am not a believer in spamming every inquirer. I know what I have here, and if this guy is making a lowball offer and won't even respond to my counter, it will be a waste of my time to follow up with him. If others on here want to spend time hounding lowball inquirers who do not even send more than one email, okay - knock yourselves out, but I have much better things to do with my time, and I am not desperate to sell anything at lowball prices.
ACTUALLY to be honest, when I get an offer, any offer high or low, I do NOT respond with a dollar figure right off the bat. I have a certain response that engages the guy, and it works for me. I am not a fan of throwing immediately my counter price out there. Engage the guy before you counter, engage him, to respond. Every response from him makes him chew on, fall in love with more, YOUR domain.
It also looks pretty weak to make a counter, and then counter even lower just because you receive no response. Why did you counter where you countered anyway? Wasn't it based on some comparables? If so, then why are you backing down if your price was justified to begin with?