U.K. 6 months visa entry Rule explanation

Dear Gurus
My wife is US citizen , she came in July 2016 in uk and 6 months leave to enter stamped on her Pasport .we stayed 3 days in London and then flew to France for holidays
Which also is visa free for US citizens.
We came back to Edinburgh on 21 July and then she stayed till 20 August 2016 she left for USA. On her arrival back on Edinburgh air port they didn't give leave to enter again.

She is is coming back to visit me again on 27th October ...
My question is that, because she came here in July 2016 and they issued 6 month leave to enter.. Was that leave expired when she left the UK ON 20th August? And this time she will get new 6 month leave to enter or still the first one is valid and she
She will have to leave in January .
I want her to stay with me 6 months but I am not sure what will happen this time , whether a new 6 month leave will start or she will have to go back.
Pls HELP. I already book the ticket for her at the END of this month. After 6 months I will apply spouse visa.
Your advise is highly appreciated
Regards

Kindly refrain from multiple repeated posts, you have answers already.