Context. The quantitative near-infrared (NIR) spectroscopic synthesis is an important technique for determining wind properties of massive stars. The Brα line is an excellent mass-loss tracer and provides valuable information on the physical conditions of intermediate-wind regions. The knowledge of the wind properties gained by studying the NIR lines could provide extra ingredients to the theory of line-driven winds, mainly because the standard theory does not predict observed properties of blue supergiants, such as high values for the β parameter (β> 2), low terminal velocities, and mass-loss variability. Aims. We seek to enhance our understanding of the wind properties of B supergiants. To this end, we propose analysing their NIR spectra over different epochs to study wind variability and its connection with phenomena arising from regions close to the photosphere. Methods. We present the first sets of multi-epoch high-resolution K- and L-band spectra of 55 Cyg acquired with the Gemini Near-InfraRed Spectrograph (GNIRS). We measured line equivalent widths and modelled the Brα line to derive (unclumped) mass-loss rates. Synthetic line profiles were computed for a homogeneous spherical wind by solving the radiative transfer equations in the co-moving frame for a multi-level atom in non-local thermodynamic equilibrium (NLTE). Results. We observe variations in the spectral lines originating in the upper photosphere and the wind. The perturbations, on average, have periods of ~13 and ~23 days; the latter is similar to that found previously from optical data (22.5 days). The NIR lines observed in 2013 are described with the same wind structure used to model a quasi-simultaneous observation in Hα. By contrast, from observations taken in 2015, we derived a higher mean mass-loss rate. Variations in the mass-loss rate are also detected within a few weeks. Interestingly, we find that the profile shape of the Hu14 line sets constraints on the mass loss. Moreover, we find the Mgâà € ¯II doublet in emission, which suggests a tenuous circumstellar gas ring or shell. Conclusions. The variability detected in the NIR H emission lines of 55 Cyg is related to changes in the mass-loss rate, which doubled its value between 2013 and 2015. Furthermore, the short-term variability (within three weeks) in the spectral lines and mass loss supports the hypothesis of strange-mode oscillations. This pilot project demonstrates the importance of comprehensive monitoring of blue supergiants™ variability to deeply understand the physical properties of their stellar winds and the role of pulsations in recurrently enhancing mass loss.