If you are to grant them an extension, I would want to know exactly what is going on. I there a conditional mortgage commitment from the bank to review?
You most likely have given them enough time to finance the home. You have signed one extension. I would have my agent get to the bottom of what is going on and what the likeliness is of closing if you do sign another extension. Things do happen and financing is tight and a lot of deals come together but it is well with in your right to know what exactly is going on.
If the risk for the buyer not to obtain a mortgage is low, I would advice you to sign the extension because it is still safer and sooner for you to close the deal. Meantime, I would have continued to do open houses and accept back-up offers from the very beginning. So if we had a buyer who could buy with cash or could close sooner, we would have had a second choice.
Do you want to sell this property? By meeting the buyer part way and giving them a little more time you may be saving this transaction. Taking a rigid stance may not yield the results you require. Listen to your agents advice....