Context. The stellar helium-to-metal enrichment ratio, ΔY/ΔZ, is a widely studied astrophysical quantity. However, its value has still not been precisely constrained. Aims. This paper is focused on studying the main sources of uncertainty that affect the ΔY/ΔZ ratio derived from the analysis of the low-main sequence (MS) stars in the solar neighborhood. Methods. The possibility of inferring the value of the helium-to-metal enrichment ratio from the study of low-MS stars relies on the dependence of the stellar luminosity and effective temperature on the initial helium and metal abundances. The ΔY/ΔZ ratio is obtained by comparing the magnitude difference between the observed stars and a reference, theoretical zero age main sequence (ZAMS) with the related theoretical magnitude differences computed from a new set of stellar models with up-to-date input physics and a fine grid of chemical compositions. A Monte Carlo approach has been used to evaluate the impact of different sources of uncertainty, i.e. observational errors, evolutionary effects, systematic uncertainties of the models. As a check of the procedure, the method was applied to a different data set, namely the low-MS of the Hyades. Results. Once a set of ZAMS and atmosphere models had been chosen, we found that the inferred value of ΔY/ΔZ is sensitive to the age of the stellar sample, even if we restricted the data set to low-luminosity stars. The lack of an accurate age estimate of low-mass field stars leads to underestimating the inferred ΔY/ΔZ of ∼2 units. On the contrary, the method firmly recovers the ΔY/ΔZ value for unevolved samples of stars like the Hyades low-MS. Adopting a solar-calibrated mixing-length parameter and the PHOENIX GAIA v2.6.1 atmospheric models, we find ΔY/ΔZ = 5.3 ± 1.4 once the age correction has been applied. The Hyades sample provided a perfectly consistent value. Conclusions. We have demonstrated that assuming that low-mass stars in the solar neighborhood can be considered as unevolved does not necessarily hold, and it may indeed lead to a bias in the inferred ΔY/ΔZ .T he effect of the still poorly constrained efficiency of the superadiabatic convection and of different atmosphere models adopted to transform luminosities and effective temperature into colors and magnitudes are also discussed.