The simultaneous effect of amplification due to cooling and damping due to resonant absorption on the kink oscillations of coronal loops is studied. The governing equation describing the kink oscillations is derived in the thin tube thin boundary layer approximation. The cooling time is assumed to be much larger than the oscillation period, and the Wentzel-Kramers-Brillouin (WKB) method is used to obtain the equation describing the dependence of the oscillation amplitude on time. This equation is solved numerically for various values of determining parameters. In particular, the question if the amplification due to cooling can balance the resonant damping and produce undamped oscillation is addressed. The conclusion is that the amplification due to cooling is not very efficient and can balance the resonant damping only when the density contrast is not very large and the cooling is very fast with the characteristic cooling time of the order of the oscillation period.
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