Context. In the past few years the number of well-sampled optical to near-infrared (NIR) light curves of long gamma-ray bursts (GRBs) has greatly increased, particularly due to simultaneous multi-band imagers such as GROND. Combining these densely sampled ground-based data sets with the Swift UVOT and XRT space observations unveils a much more complex afterglow evolution than what was predicted by the most commonly invoked theoretical models. GRB 100814A represents a remarkable example of these interesting well-sampled events, showing a prominent late-time rebrightening in the optical to NIR bands and a complex spectral evolution. This represents a unique laboratory to test the different afterglow emission models. Aims: Here we study the nature of the complex afterglow emission of GRB 100814A in the framework of different theoretical models. Moreover, we compare the late-time chromatic rebrightening with those observed in other well-sampled long GRBs. Methods: We analysed the optical and NIR observations obtained with the seven-channel Gamma-Ray burst Optical and Near-infrared Detector (GROND) at the 2.2 m MPG/ESO telescope together with the X-ray and UV data detected by the instruments onboard the Swift observatory. The broad-band afterglow evolution, achieved by constructing multi-instrument light curves and spectral energy distributions, is discussed in the framework of different theoretical models. Results: We find that the standard models that describe the broad-band afterglow emission within the external shock scenario fail to describe the complex evolution of GRB 100814A, and therefore more complex scenarios must be invoked. The analysis of the very well sampled broad-band light curve of GRB 100814A allowed us to deduce that models invoking late-time activity of the central engine in the observed afterglow emission are the preferred ones for all the different observed features. This late-time activity most likely has the form of a delayed reactivation of the ejecta emission process. However, a more detailed modelling of the radiative mechanisms associated with these scenarios is necessary to arrive at a firm conclusion on the nature of the optical rebrightenings that so often are detected in long GRBs.