Context. The search for planets orbiting metal-poor stars is of utmost importance for our understanding of planet formation models. However, no dedicated searches have been conducted so far for very low mass planets orbiting such objects. Only a few cases of low-mass planets orbiting metal-poor stars are thus known. Amongst these, HD 41248 is a metal-poor, solar-type star on the orbit of which a resonant pair of super-Earth-like planets has been announced. This detection was based on 62 radial velocity measurements obtained with the HARPS spectrograph (public data). Aims: We present a new planet search program that is using the HARPS spectrograph to search for Neptunes and super-Earths that orbit a sample of metal-poor FGK dwarfs. We then present a detailed analysis of 162 additional radial velocity measurements of HD 41248, obtained within this program, with the goal of confirming the existence of the proposed planetary system. Methods: We analysed the precise radial velocities, obtained with the HARPS spectrograph, together with several stellar activity diagnostics and line profile indicators. Results: A careful analysis shows no evidence for the planetary system. One of the signals, with a period of ~25 days, is shown to be related to the rotational period of the star, and is clearly seen in some of the activity proxies. We were unable to convincingly retrieve the remaining signal (P ~ 18 days) in the new dataset. Conclusions: We discuss possible causes for the complex (evolving) signals observed in the data of HD 41248, proposing that they might be explained by the appearance and disappearance of active regions on the surface of a star with strong differential rotation, or by a combination of the sparse data sampling and active region evolution. Based on observations collected at ESO facilities under programs 082.C-0212, 085.C-0063, 086.C-0284, and 190.C-0027 (with the HARPS spectrograph at the ESO 3.6-m telescope, La Silla-Paranal Observatory).Table 1 is available in electronic form at http://www.aanda.orgRadial velocity data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/566/A35