Lord Chief Justice Lord Burnett and two other leading judges will announce their decision in his case on Wednesday morning at the Court of Appeal.
The judges have been urged to overturn contempt of court findings against Robinson, 35, whose real name is Stephen Christopher Yaxley-Lennon.
At a hearing earlier this month, his QC Jeremy Dein argued that procedural "deficiencies" had given rise to "prejudice".
Mr Dein also submitted that the sentence was "manifestly excessive" and "insufficient" regard had been given to personal mitigation.
Robinson was jailed in May after he filmed people involved in a criminal trial outside Leeds Crown Court and broadcast the footage on social media.
The footage, lasting around an hour, was watched 250,000 times within hours of being posted on Facebook.
The far-right activist was given 10 months for contempt of court, which he admitted, and a further three months for breaching a previous suspended sentence.
Robinson was detained outside the court after using social media to broadcast details of a trial which is subject to blanket reporting restrictions.
Jailing him, Judge Geoffrey Marson told Robinson his actions could cause the trial to be rerun, costing "hundreds and hundreds of thousands of pounds".
The judge said it was a "serious aggravating feature" that he was encouraging others to share it and it had been shared widely.
He added: "Everyone understands the right to freedom of speech but there are responsibilities and obligations.
"I am not sure you appreciate the potential consequence of what you have done. People have to understand that if they breach court orders there will be very real consequences."
It was the second time Robinson had breached court orders, having narrowly avoided jail in May last year over footage he filmed during the trial of four men who were later convicted of gang-raping a teenage girl.
The judge on that occasion gave him a three-month suspended sentence and told him his punishment was not about "freedom of speech or freedom of the press" but about "justice and ensuring that a trial can be carried out justly and fairly".
Mr Dein argued during the recent appeal proceedings that the findings of contempt of court on each occasion should be quashed as a "conglomeration of procedural deficiencies" had given rise to prejudice.
The QC said the proceedings in Leeds had been "unnecessarily and unjustifiably rushed".
He told the judges: "We maintain it is of particular importance that right from the outset the appellant, albeit in a very stressful and difficult situation, offered to have the live stream taken down and contact people who could do so."
There had been no intention to disrupt the trial or to breach any order, Mr Dein said.