There is still a lot of confusion on this thread about the legal position and as Diane says, the question can't really be answered until the OP has got the item back and inspected it to see what is wrong and what caused the damage. But the OP has been reluctant to do this from the start so everything else is speculative.
Diane's post doesn't make general matters any clearer in that it doesn't address the issue of acceptance of the goods and the fact that they were in working order on sale. And no-one knows exactly why the microwave isn't working. It's either because it is faulty or because it has been misused.
The period of six months during which it can be implied that goods were not working at the point of sale can be rebutted if the goods were proven to be working/of merchantable quality on sale - in this case, from the correspondence the OP has had with the buyer, we know that the microwave was working for the first two months. It only broke down later.
So the right to reject the goods doesn't necessarily apply because they were working on purchase
and have been proven to be working.
From the Sale of Goods Act:
s. 48A
(1)This section applies if—
(a)the buyer deals as consumer ... and
(b)the goods do not conform to the contract of sale at the time of delivery.
(2)If this section applies, the buyer has the right—
(a)under and in accordance with section 48B below, to require the seller to repair or replace the goods, or
(b)under and in accordance with section 48C below—
(i)to require the seller to reduce the purchase price of the goods to the buyer by an appropriate amount, or
(ii)to rescind the contract with regard to the goods in question.
(3)For the purposes of subsection (1)(b) above goods which do not conform to the contract of sale at any time within the period of six months starting with the date on which the goods were delivered to the buyer must be taken not to have so conformed at that date.
(4)Subsection (3) above does not apply if—
(a)it is established that the goods did so conform at that date;
(b)its application is incompatible with the nature of the goods or the nature of the lack of conformity.
Assuming, however, that we give the buyer the benefit of the doubt and assume that the microwave was of poor quality and broke down after two months through no fault of the buyer then we must look at s.48B.
48B
(1)If section 48A above applies, the buyer may require the seller—
(a) to repair the goods, or
(b) to replace the goods.
(2)If the buyer requires the seller to repair or replace the goods, the seller must—
(a)repair or, as the case may be, replace the goods within a reasonable time but without causing significant inconvenience to the buyer;
(b)bear any necessary costs incurred in doing so (including in particular the cost of any labour, materials or postage).
(3)The buyer must not require the seller to repair or, as the case may be, replace the goods if that remedy is—
(a)impossible, or
(b)disproportionate in comparison to the other of those remedies, or
(c)disproportionate in comparison to an appropriate reduction in the purchase price under paragraph (a), or rescission under paragraph (b), of section 48C(1) below.
(4)One remedy is disproportionate in comparison to the other if the one imposes costs on the seller which, in comparison to those imposed on him by the other, are unreasonable, taking into account—
(a)the value which the goods would have if they conformed to the contract of sale,
(b)the significance of the lack of conformity, and
(c)whether the other remedy could be effected without significant inconvenience to the buyer.
(5)Any question as to what is a reasonable time or significant inconvenience is to be determined by reference to—
(a)the nature of the goods, and
(b)the purpose for which the goods were acquired.
We then need to look at s.48(C). This says that the buyer may require a reduction in the purchase price or a rescission of the contract where:
the condition in subsection (2) below is satisfied.
(2)The condition is that—
(a)by virtue of section 48B(3) above the buyer may require neither repair nor replacement of the goods; or
(b)the buyer has required the seller to repair or replace the goods, but the seller is in breach of the requirement of section 48B(2)(a) above to do so within a reasonable time and without significant inconvenience to the buyer.
I could be wrong (it is very poorly drafted) but I read that as saying that the Buyer can only ask for a reduction in the purchase price or rescission of the contract if the buyer is not permitted to ask for a repair or replacement because it is either impossible or disproportionately expensive or will be a significant inconvenience to the buyer compared to getting a reduction or a refund.
Furthermore, even if the buyer does ask for a refund or price reduction, then the Seller is entitled to discount it:
(3)For the purposes of this Part, if the buyer rescinds the contract, any reimbursement to the buyer may be reduced to take account of the use he has had of the goods since they were delivered to him.
This is my understanding of the law and reflects the advice given by Trading Standards and the Which Consumer organisation. If anyone thinks any differently, I would be happy to discuss and be proved wrong.
Incidentally, the consumer legislation is being redrafted at the moment so I hope all will become clearer when the new legislation comes into force.
I would reiterate though that the OP should take a commercial view and offer the buyer a refund in whole or in part.
you took advice from rude loud mouths that didn't have a clue
I hope that didn't refer to me....