When your house has been on the market for quite a while and you have already dropped your initial asking price, it can come as quite a shock to get an offer to purchase for even less than the reduced amount.
But before you get angry and reject the offer out of hand as being insulting, you should try to remember that you actually just won the lottery. Out of all the homes currently on the market, this buyer decided to make an offer on yours.
And before that happened, he or she very likely did their own market research, got bond approval for a certain amount, and visited and compared several homes for sale in the correct price range.
All he or she is trying to do now is buy the home they liked the most (yours), for the lowest price possible - which means that the best way to treat the offer is as the "opening bid" in a negotiation. So before you start losing sleep about why they think your home is worth so little, start thinking about what your counter offer should be.
In order to work this out, you need to do two things, the first of which is to get your agent to find out what it is about your home that the buyer does not like and resulted in the lower-than-expected offer. If it's deferred maintenance or dated décor, you can negotiate around fixing certain problems in return for a better offer.
Alternatively, you can establish what it would cost to address those problems, and to hold the property while you do, and decide to accept the offer in return for saving those costs and achieving a quicker sale.
Secondly, you need to ask your agent for a new Comparative Market Analysis and take a fresh look at the market - especially if the condition of your home is not the problem. A lot can happen in a few months and if prices have been under pressure, the offer may actually be better, in relative terms, than you thought. What is more, you will then also be justified in making a lower offer on your next house.
In short, you need to keep your eyes on the prize, and remember that right now, this buyer and this offer is your best chance of obtaining that prize, so you need to keep them in the game.
At the same time, you need to accept that he or she also has goals to meet and limitations on what they can spend. So be pleasant, be honest and above all be reasonable while your agent negotiates to try to help you both get what you want.