Bance, who plays for Mainz in the Bundesliga, did not arrive at the start of the team's pre-tournament training camp in Portugal this week, Burkinabe Football Federation officials said.
The 25-year-old striker had earlier this month told Burkinabe television he would not make himself available for selection, saying Duarte had paid him scant attention over the past year, making no phone contact nor watching any of his club matches.
Burkina Faso have been drawn in Group B along with Ghana, the Ivory Coast and Togo. The Nations Cup is being hosted in Angola from January 10-31.
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