Context. The identification of the progenitors of Type Ia supernovae (SNIa) is extremely important in several astrophysical contexts, ranging from stellar evolution in close binary systems to evaluating cosmological parameters. Determining the distribution of the delay times (DTD) of SNIa progenitors can shed light on their nature. The DTD can be constrained by analysing the correlation between the SNIa rate and those properties of the parent galaxy which trace the average age of their stellar populations. Aims. We investigate the diagnostic capabilities of this correlation by examining its systematics with the various parameters at play: simple stellar population models, the adopted description for the star formation history (SFH) in galaxies, and the way in which the masses of the galaxies are evaluated. Methods. We computed models for the diagnostic correlations for a variety of input ingredients and for a few astrophysically motivated DTD laws appropriate for a wide range of possibilities for the SNIa progenitors. The models are compared to the results of three independent observational surveys. Results. The scaling of the SNIa rate with the properties of the parent galaxy is sensitive to all input ingredients mentioned above. This is a severe limitation on the possibility to discriminate alternative DTDs. In addition, current surveys show some discrepancies for the reddest and bluest galaxies, likely because of limited statistics and the inhomogeneity of the observations. For galaxies with intermediate colours the rates are in agreement, leading to a robust determination of the productivity of SNIa from stellar populations of ≃0.8 events per 1000 M_⊙. Conclusions. Large stastistics of SNIa events along with accurate measurements of the SFH in the galaxies are required to derive firm constraints on the DTD. The LSST will achieve these results by providing a homogeneous, unbiased, and vast database on both SNIa and galaxies.