Rasmussen began the 2003–04 Danish Superliga season as starting goalkeeper, but lost his place to Pedersen in April 2004 following a slump in form. He was second choice for the 2004–05 Danish Superliga season, but following an injury to Pedersen in April 2005, Rasmussen got another chance and again established himself in the starting line-up.
Rasmussen started as the goalkeeper for the 2003-04 Danish Superliga season, but lost his position to Pedersen in April 2004 due to a decline in form. He was second choice for the 2004-05 season, but after Pedersen got injured in April 2005, Rasmussen regained his starting spot and became the regular goalkeeper.