Honestly, I think it is pretty impossible for any of us here to give you any valid advice without knowing all of the specifics of your situation. There are so many things that can affect a home sale. If there is a high level of radon, then you need to get that remediated right away, both in terms of selling the home and in terms of you living in the home. As far as the rest, there are just so many variables that could make a difference. Maybe you need to fix the issues or maybe these people are just being ridiculous. How much money are you talking about for these repairs they are demanding?
One question is why your home has been on the market for so long without another offer. There are so many specific reasons that could be. 1. Is the market where you are just in really bad shape right now where nothing is selling; 2. Did you over price the house to begin with (even if other houses in the neighborhood are selling at those prices are the details of your house comparable- i.e. did those other houses have updated interiors; granite counters; better yards etc while yours doen't); 3. Is there some issue with your house that has led to a lack of offers-- i.e. poor curb appeal; no yard; issues with lay out; not updated or doesn't have the type of interior perks that other houses in the neighborhood have.; 4. Could the items the inspector found be what is keeping you from getting offers or keeping you from getting offers in the range you want?
I live in a part of town that is very desirable because of the schools. A lot of people want their kids in one of 3 specific grade schools. As a result, houses of all sizes (smallish to large) in the area can often sell in less than a week. In fact, I have a friend, who is trying to move into the area who has already lost 2 houses he wanted because he didn't get his offers in fast enough. Even so, there are houses here that are on the market for 6 months to a year or more and there is usually a reason. Some of the reasons are things that can't be changed. There was an absolutely gorgeous house- but the entire backyard was pool and concrete- no grass at all- not great for kids or dogs. That house sat on the market for a year and a half; Some are just priced wrong- I can think of another beautiful house that sat on the market for over a year- the reason was it was a big house that had an absolutely tiny back yard, and was totally overpriced and the owners didn't want to bring the price down. Some is is stuff that the owners didn't want to put the money into fixing- yet they still priced their house the same as others in the area that did not have those issues and didn't want to make concessions - For, example there was a house where you walked in and it smelled hugely like cat (the carpets I'm pretty sure) and all the doors were beat up/scratched up. They didn't want to do a carpet allowance. I can think of another one that still had all of its original appliances, laminate counters, and even vinyl floors and they wanted the same price as ones in the neighborhood were selling for that had been updated with new appliances, granite counters, and wood or tile floors. The house just didn't have the appeal of others in the neighborhood which were selling for the same price they were asking.
Any buyer, is going to figure up what the cost is to fix any issues they see in the house- whether that be updates, carpets, cosmetic issues, etc. - and if it is going to cost them more to fix the issues than it would to buy another comparable house for that price in the same neighborhood, unless they absolutely are in love with your house, they won't buy it. So I think you need to really analyze what the issues might be with your house, that might be turning buyers off, if any. Your buyers possibly are just being unreasonable, but you may actually have issues that need to be taken care of, or accounted for before you are going to get a good sale. It is really hard to say whether your buyers are being unreasonable without knowing the specifics of what they are asking you to do.