Incompetent Estate Agent - Do we still have to pay him?

I'm a bit confused by this thread.

Once the EA has found a buyer - this is clearly his responsability - and the matter has been put in the hand of the solicitors, who's responsibile for further progress - the EA, the solicitor, the vendor/buyer, everybody and nobody ? This doesn't seem very clear.

How far does the EA's responsability go in initially vetting the buyer and his readiness/suitability for the amount and timing of the sale ?

Is this specified in the contract between the vendor and the EA ?

My impression of the responsibilities is the following:
The vendor puts their property on the market via an Estate Agent
The Estate Agent undertakes to market and negotiate the best possible price on behalf of the vendor
On completion of the negotiation, the purchaser undertakes to purchase the property.
It is at this point that I think that the scope of the Estate Agent becomes grey. A good Estate Agent will follow through on the progress of the legals of the sale of the property in order to bring it to a close within a set period of time. But I'm not sure that it is actually part of their job! In a property chain, as has been quite rightly pointed out, there are many links and if one fails or isn't up to scratch then the progress will be slowed down.
I'm not sure in this case that the Estate Agent is physically at fault - their hands are tied if the purchasers are holding it up from their end. But they have to act on your instructions as you are the clients. Have you issued or has your solicitor issued a notice that if they don't sign contracts/close within a set period of time that you will put the property back on the market?