Hello, I am a solicitor with 20 years experience. I will try to help you with this.
Am I right i thinking they haven't carried out the repair yet?
I think you are right it must be fit fir purpose and last a reasonable length of time. If it isn't fit for purpose then you can take it back and demand a refund or a replacement. usually you wold need to take it back within 4 weeks of purchase but as you have already gone to them for help and a second problem has arisen being outside 4 weeks should not prevent a full refund.
You should return it as soon as possible though.
The law protecting you is The Sale of Goods Act 1979.