In this work, we consider the execution of applications on desktop grids. Such parallel systems use idle computing resources of desktops distributed over the Internet for running massively parallel computations. The applications are composed of workflows of independent non-preemptive sequential jobs that are submitted by successive batches. Then, the corresponding jobs are executed on the distributed available resources according to some scheduling policy. However, most resources are not continuously available over time since the users give their idle CPU time only for some time when they are not using their desktops. Moreover, even if the dates of unavailability periods are estimated in advance, they are subject to uncertainties. This may drastically impact the global performances by delaying the completion time of the applications. The aim of this paper is to study how to schedule efficiently a set of jobs in the presence of unavailability periods on identical machines. In the same time, we are interested in reducing the impact of disturbances on the unavailability periods. This is achieved by maximizing the stability that measures the distance between the makespan of the disturbed instance over the initial one. Our main contribution is the design of a new parametrized algorithm and the analysis of its performance through structural properties. This algorithm reduces the impact of disturbances on availability periods without worsening too much the makespan. Its interest is assessed by running simulations based on realistic workflows. Moreover, theoretical results are obtained under the assumption that the size of every availability interval is at least twice the size of the largest job.