Low Earth Orbit (LEO) satellite communications can provide real-time services with reduced latency, which makes them ideal for applications requiring timeliness, such as Internet connectivity, remote monitoring, and disaster response. In this paper, we study a problem of information freshness optimization for such a scenario. Usually, this is quantified through the age of information (AoI) metric, but the typical scenarios involve a homogeneous time horizon, where transmission can take place indifferently at any instant. In reality, LEO communication may be severely influenced by its intermittent connectivity, which is not present for long time windows where line of sight with the satellite system is absent. Thus, we consider a problem of AoI-minimal scheduling for a finite horizon, solved via dynamic programming, where intermittent connectivity is accounted for, and addressed through different approaches. Moreover, we quantitatively evaluate the impact of different parameters on AoI and derive practical considerations for empirical setups.