I am always a little suspicious when sellers change agents, that either their price is too high OR what will the new agent do differently? I always think that if a house is sensibly priced and on rightmove/zoopla then it will sell, pretty much regardless of how much effort an agent takes to shift it.
However that is a bit simplistic and in your case I really can't see that this is the case - there is obviously an issue somewhere with your agents process (by this I mean how they are progressing the sale, not their marketing) if this has fallen through this many times. If there was an issue with the price then it wouldn't have sold 3 times!
Is there ANYTHING to do with the property that is making people pull out. Who are these people who put in offers (thereby showing their interest and commitment in actually purchasing the property) and then withdraw. What makes them walk away, or choose another property? How good is your solicitor? They also need to be pushing the sale through, and on the ball to spot any signs of a nervous buyer.
Who is buying the property? Is it first time buyers/chains/investors? And what sort of property - detached/semi/town/rural/how many beds?
Unfortunately there is so much uncertainty at the moment, with Brexit etc . I'm so sorry this is happening to you, it must be so incredibly stressful.
Sorry for the mega long post. I am not an EA, just a property junkie also trying to buy at the moment (love the house so much I daren't post in case I jinx it).