The DSG box was the reason I got rid of my Audi TT. It had done 90,000 and started showing signs of the dreaded fault that after research suggested a repair cost of anywhere between £1,800 and £4,500. Ended up trading it in before it went kaput.
It's normally the Mechatronic unit (the electronic brain) that goes rather than the gearbox itself. When I was looking into it, there was a small number of companies that were offering repairs to the Mechatronic unit but it was a new thing & I didn't really trust it before it had shown to work under the test of time, so it might be worth looking into.
By the way, the DSG warranty in the USA was extended to 100,000 miles due to the amount of lawsuits and the number of faults, yet VAG Europe refused to follow suit and admit there was an inherent fault.
I'd never buy another DSG because of this but I wish you the best of luck getting it sorted.
Steve