The problem of estimation of the shape parameter in a generalized half-logistic distribution for progressively type-II censored samples is of interest in reliability and survival analysis. In this paper, Bayesian methods of estimation based on quadratic and Linex loss functions are proposed. Closed expressions and approximations are obtained for the Bayes and posterior risks of Bayes estimators. These results allow us to assess the performance of estimators obtained under the previously cited loss functions. An application to a real dataset and a simulation study are included where the importance of the different features involved in the progressive type-II censoring scheme is also shown.