Oh Boy! sounds like a tyre kicker, and yes you must deal with them as you see fit.

Once they start to try to keep haggling and all the argy bargy it soon becomes clear what sort of buyer they really are, and probably not worth the time and effort.

We usually only give them one chance to accept either the offer we send back, that they were trying to find out, or accept what they are offering, or just say thanks for their interest but "No".

But we never ignore or are rude.

We are always happy to deal/negotiate with someone who is polite, as you were with your enquiry, and presume other sellers are the same. After all, the name of the game is to sell, so if there is a chance of a sale at a price we are happy with, don't really care how we got the sale as long as it is not breaking any rules.  

We always reply with an answer and if we send an offer, it is always our "best and final". Usually either don't hear back or they accept.

Either way we are happy.