Moving through a dynamic world, humans need to intermittently stabilize gaze targets on their retina to process visual information. Overt attention being thus split into discrete intervals, the automatic detection of such fixation events is paramount to downstream analysis in many eye-tracking studies. Standard algorithms tackle this challenge in the limiting case of little to no head motion. In this static scenario, which is approximately realized for most remote eye-tracking systems, it amounts to detecting periods of relative eye stillness. In contrast, head-mounted eye trackers allow for experiments with subjects moving naturally in everyday environments. Detecting fixations in these dynamic scenarios is more challenging, since gaze-stabilizing eye movements need to be reliably distinguished from non-fixational gaze shifts. Here, we propose several strategies for enhancing existing algorithms developed for fixation detection in the static case to allow for robust fixation detection in dynamic real-world scenarios recorded with head-mounted eye trackers. Specifically, we consider (i) an optic-flow-based compensation stage explicitly accounting for stabilizing eye movements during head motion, (ii) an adaptive adjustment of algorithm sensitivity according to head-motion intensity, and (iii) a coherent tuning of all algorithm parameters. Introducing a new hand-labeled dataset, recorded with the Pupil Invisible glasses by Pupil Labs, we investigate their individual contributions. The dataset comprises both static and dynamic scenarios and is made publicly available. We show that a combination of all proposed strategies improves standard thresholding algorithms and outperforms previous approaches to fixation detection in head-mounted eye tracking.