Time-resolved X-ray absorption spectroscopy (tr-XAS) has been shown to be a versatile measurement technique for investigating non-equilibrium dynamics. Novel X-ray free electron laser (XFEL) facilities like the European XFEL offer increased repetition rates for stroboscopic XAS experiments through a burst operation mode, which enables measurements with up to 4.5 MHz. These higher repetition rates lead to higher data acquisition rates but can also introduce long-lived excitations that persist and thus build up during each burst. Here, we report on such long-lived effects in Ni and NiO thin film samples that were measured at the European XFEL. We disentangle the long-lived excitations from the initial pump-induced change and perform a detailed modelling-based analysis of how they modify transient X-ray spectra. As a result, we link the long-lived effects in Ni to a local temperature increase, as well as the effects in NiO to excited charge carrier trapping through polaron formation. In addition, we present possible correction methods, as well as discuss ways in which the effects of these long-lived excitations could be minimized for future time-resolved X-ray absorption spectroscopy measurements.