Elder, who resigned from Solid Energy this year, and Arseneau, on leave from Arts Management, are overseas and could not be contacted. Representatives from Solid Energy and the orchestra said any potential conflict of interest was managed.
Engineering, Printing and Manufacturing Union assistant national secretary Ged O'Connell said spending $15.3 million on sponsorship in 11 years was a concern.
Along with spending on bonuses and vehicles, it was another example of the "poor management" which cost hundreds of jobs, he said.
Labour's state-owned enterprises spokesman, Clayton Cosgrove, agreed with Solid Energy supporting its community.
But he said it should have ended when the company's dire financial position became apparent.
Arts Management acting executive chairman Richard Ballantyne said Arseneau had no earlier involvement in the Christchurch Symphony Orchestra, or Southern Opera, before 2010.
She revealed she was married to Elder and ways of managing conflict of interest problems were agreed.
Solid Energy stakeholder relations manager Vicki Blyth said the $15.3m donated represented 0.2 per cent of the company's total revenue of $6.7 billion between 2001 and June 2012.
Asked what those who lost their jobs might think about the donations, she said: "Hindsight's a fantastic thing.
"When you look at our accounts, it's only last year the company made a loss; prior to that it was returning reasonable profits."