The Court of Appeal rejected an application to have Mr Justice Fraser removed from the case, after the Post Office accused him of being biased. It had previously made an application for him to stand down from the hearings.
A group of 557 former post office staff, including Telford's Tracy Felstead, are taking legal action against the company in an attempt to clear their names.
Miss Felstead, 37, from Brookside, was jailed for six months in 2001 after being convicted of stealing £11,500 when she was a 19-year-old counter clerk. She protests her innocence, and says a glitch with the Post Office's Horizon computer system created the shortfall.
Judge Fraser was appointed last year to hear four separate trials relating to the claims.
The first trial, which ended in March this year, looked at the contractual arrangement between the Post Office and its sub-postmasters. The judge found in favour of the workers, although the Post Office has said it will appeal.
The second trial, which began in March, looks at the Horizon computer system itself, and is due to resume on June 4.
Rubbina Shaheen, the former sub-postmistress of Greenfields Post Office in Shrewsbury, is also fighting to clear her name after being jailed for 12 months in 2010 for false accounting.
Mrs Shaheen, 53, who now lives in Worthen, near Shrewsbury, is not part of the High Court action, but is seeking to have her conviction overturned through the Criminal Cases Review Commission.
Miss Felstead is also seeking to have her conviction overturned.
The High Court action, which is expected to continue into next year, has been brought by Justice For the Subpostmasters Alliance (JFSA). The organisation was set up to represent post office workers who claim they were falsely accused due to a fault with the Horizon system.
The Post Office insisted there was not a problem with the Horizon system.
“We have confidence in Horizon, which is robust, reliable and used across 11,500 branches by postmasters, agents and their many thousands of staff to process millions of transactions successfully every day, including on behalf of the UK’s high street banks,” it said.
The trial continues.