Does it make sense to "ignore low ball offers"?

If it’s really low ( under 30%), I’ll ignore them. If it’s reasonable, I’ll counter. What I won’t respond to is when the prospective buyer asks me “ what’s your lowest”? Figure it out genius. That usually ends the conversation. 
 

I think it depends on how low the balls are. 

If I list an item and get some insanely stupid offer I ignore it. If the offer is 1/2 my ask and the buyer gives some justification why his # is what it is (ie: "The Audiogon blue book says...." ) I'm encouraged that the buyer is both real and educated. I can work with that. 

Some listings are a joke. When some egocentric Malthusian lists his 20 year old worn out amp for what it retailed for 20 years ago it's nearly useless to negotiate. He's seeking validation and not a sale. These types get all huffy when you offer a real world FMV. 

Interestingly, an appraiser told me once that an item that sells at an auction is worth the second highest bid.  Considering that a bit it made perfect sense.

Assuming properly exposed to the market, in the end an item is worth what someone will pay for it. 

Odd how some take it as a personal insult, it's simply business...I simply decline their offer and find that the serious potential buyers will simply make a better offer...I don't counter because the Audiogon system require long wait for them to respond, and they usually do not respond...

Do you need to sell it? Are you desperate? If so then respond. If it’s a ridiculous offer I’ll respond with a higher amount than what it is listed for. Most of the time I don’t respond. House bids are different, the realtor has to submit the offer, but the seller does not have to respond. The buyers realtor will tell the buyer to make a bid good enough to get a counter to get negotiating started.

I don’t need to sell to buy what I want so I can sit on the piece for a while. Eventually everything sells.

Sometimes peoples expectations of a given price is unrealistic. Years ago I made an offer to a guy whose response was "go to hell". After a month or so he realized my offer was actually more than fair. He wanted to accept it. I told him that his "go to hell" attitude suggested that I take my business elsewhere.