Mr Pearson is demanding that the union divulges the names of its members who passed on allegations of mismanagement in 1994, which he claims defamed him.
The EIS sent the document to the Scottish Office, which cleared the college leadership of the most serious charges.
Lord Cameron rejected Mr Pearson's case last year. Now three appeal judges have upheld his ruling that Mr Pearson could not prove malice lay behind the union moves and that communications between a union and its members are privileged.
The college announced in January that Mr Pearson was stepping down so he could "to take up new challenges".