Data on a prolonged period of EUV emission after a sudden rise in brightness recorded by the Extreme Ultraviolet Explorer (EUVE) for the star AU Mic are discussed. Intense emission was observed for roughly 12 hours after each of two impulses, which exceeds by 10 times the radiation cooling time of coronal loops with typical flare plasma densities. Difficulties are pointed out for two explanations for this phenomena suggested earlier: emission by dense loops in the main phase of the flare, and emission of rarified plasma in coronal transients. Joint analysis of observations of the 65-190 A band and the 93.9 A Fe XVIII line showed a temporary change in the emission measure of the source. The total energy emitted during approximately 12 hours was 3 x 10 exp 35 erg. The concept of post-eruptive energy release is used to explain the prolonged emission in the EUV. The source of the emission is a system of high coronal loops with size exceeding the radius of the star. Such loop systems of already-cooled plasma have been observed on the sun in H-alpha during powerful flares (for example, June 15, 1991) after the transient has gone. Some additional energy input into the loop system from vertical current layers is possible, which prolongs the emission. The proposed phenomenon is a new type of surface activity on late stars, which is intermediate between impulsive flares on red dwarfs and prolonged and powerful events on the subgiant components of RS CVn double systems.