This paper addresses the permutation flowshop scheduling problem with availability constraints where the machines are not available cyclically and the starting and finishing times of the periodic unavailability intervals are known in advance. In our case, this constraint is due to the shift calendar in a company in the aerospace industry, where all machines must stop at the same time (shift changes, nights, weekends, etc.). In this company, shifts are formed by different teams of workers, and having one worker to complete the tasks of another worker is not desirable in terms of efficiency and quality of the operation. In the literature, this cyclical constraint is also reported due to preventive deterministic and fixed maintenance activities. For this reason, this constraint is known as periodic maintenance, and –to the best of our knowledge– it has been addressed for the single machine and parallel machines layouts, but not for the flowshop. For this layout, it can be observed that different scheduling problems may arise depending on the assumptions about the preemption of the operations. In our case, the preemption of operations is not allowed, and therefore, if an operation cannot be finished within the current availability period, then it should be scheduled in the next one. For this problem, the objective considered is the makespan minimisation. The structure and hardness of the problem depending on the size of the availability periods is studied using Mixed Integer Linear Programming and complete enumeration, in order to determine the range of values for the availability period that makes the problem under consideration to be substantially different than its classical (unconstrained) counterpart. For these cases, specific heuristics with different computational complexity are developed, and an extensive computational experience is carried out to establish the efficiency of the proposed heuristics. Additionally, an iterated greedy metaheuristic is employed, showing excellent results.