I strongly suggest that when you write your offer you do your homework first. Find out what the owner paid for the home and what their mortgage is on it. All too often these days, sellers are upside down yet trying to sell without taking a loss.
Have your agent try to find out what the seller's motivation is. Do they have to sell? Or are they thinking they will rent it out if it doesn't sell?
How strong is your credit and cash position? Typically, the more cash you have, the more desirably your offer will be...If you are only doing 3.5% FHA loan, you will likely have to go a bit higher than someone with cash.
A typical buyer mistake is to pick a number out of a hat and just write it up...do your homework first and you stand much greater chance of getting the home you want!
If the house has been on the market a long time, why wouldn't you make a lower offer? That said, keep in mind that every seller is different - how realistic they are about their house's value, their emotional commitment to selling, their equity position, etc... A great agent/broker can help figure all that out and craft an offer that is likeliest to get you the best price you can get on the house without insulting the seller to the point where they won't do business with you at any price.
If I was representing the Buyer, I would advise them that the #1 reason why it was there so long, was that the LISTING PRICE was too high; no question.
Naturally, I would want to do an updated CMA to see where the LISTING PRICE should have been, and where the Offering Price should be:
But the Seller abviously, have not been listening to their Agent, they have an inflated sense of what their house is worth, and they need to be brought back to reality.
If that is the case, they may be offended by that reality; but someone has to make them listen.
They probably will blame it on their Listing Agent, and say he wasn't doing a good job of marketing it.
Talk to your Realtor.