What to do with very low offer on an item for sale

I'd response by saying "Here is the lowest I am willing to go: $xxx."  Take it or leave it.  But don't ask for further negotiation.

It’s your item, your listing if you feel it is an unreasonable offer just ignore it 

Simple. Ignore it. 

I will respectfully disagree with the people who say "ignore it". I say this based on my career, where I earned my income on100% commission.  Some have used the term negotiation 101 and given their answer.  I would start with Selling 101 first. How did you determine your selling price?  Choosing a selling price is not based on what others are asking, but on researching what the item you’re selling has sold for in the last 90 days. Now that you know the true Market Value, you can choose your selling price. Personally, I set the price 20% above market value, leaving room to negotiate.
On to negotiations.  I always start by thanking the person for their interest/offer (as you did) and then invite them to negotiate with me.  As in "Thank you very much for your offer. I believe I have priced the xyz competitively; however, do you have any flexibility on your offer?"  No response? Then someone is just fishing, which is ok. Some cultures start with an aggressive offer. Getting any offer means there is interest in what you are selling. No offers is telling the seller that they love their item more than a buyer.

Here's two things that make me want to tie someone up in a chair, beat them with a monkey wrench and make them listen to the soundtrack of "Annie" on an endless loop.

Take the guy that's selling a 5 year old piece of gear that listed for $5,000.00 when it was brand new. He's asking $2,500.00 for the item. His title reads... "Oompa Doompa Class Z Power Amp 50% off!

Hey stupid. It's only 50% off if it's brand new, not 5 years old.

Secondly, the line "Lowballs Will Be Politely Ignored." Guess what? It's too late. You've just acknowledged the lowballers by including that line in your ad.

Stop it. I implore you.