NGC 5408 X-1 is a well-studied ultraluminous X-ray source (ULX) that has been seen to emit in X-rays persistently above the Eddington limit of a stellar mass black hole for years. In this paper we report on the most extensive X-ray monitoring of a ULX, using more than 4 yr of observations from the Swift satellite. We find that the 115 d periodicity reported by Strohmayer disappeared after only a few cycles, confirming the suspicion of Foster et al. that the periodicity is most likely superorbital and not the orbital period of the system. We also report on a clear dipping behaviour of the source that may be related to a (super)orbital phenomenon. All these features are reminiscent of Galactic X-ray binaries and strengthen their link with ULXs. Deeper observations of a dip could help resolve the ambiguity about the interpretation of the spectral components of ULXs.