We investigate resource allocation for a movable antenna (MA) enabled integrated sensing and communication (ISAC) system scanning a sector for sensing and simultaneously serving multiple communication users using multiple variable-length snapshots. To tackle the critical challenges of slow antenna movement speed, dynamic radar cross section (RCS) variation, imperfect channel state information (CSI), and finite precision antenna positioning encountered in practice, we propose a novel two-timescale (TTS) optimization framework. In particular, we jointly optimize the discrete MA positions, the communication and sensing beamforming vectors, and the snapshot durations for minimization of the average transmit power at the base station (BS) while guaranteeing a minimum sensing and communication quality of service (QoS) and accounting for imperfect CSI. To overcome the slow antenna movement speed, the MA positions are adjusted only once per scanning period whereas the beamforming vectors and snapshot durations are adapted in every snapshot. Furthermore, to manage the impact of varying RCSs, a novel chance constraint for the sensing QoS is introduced. To solve the resulting challenging highly non-convex mixed integer non-linear program (MINLP), an efficient iterative algorithm exploiting alternative optimization (AO) is developed and shown to yield a high-quality suboptimal solution. Our simulation results reveal that the proposed MA enabled ISAC system cannot only significantly reduce the BS transmit power compared to systems relying on fixed-position antennas and antenna selection but also exhibits a remarkable robustness to RCS fluctuations and imperfect CSI. Furthermore, the proposed TTS framework achieves a similar performance as a system adjusting the MA positions in every snapshot, while the TTS approach significantly reduces the time used for MA adjustment.