Calcium alternans is a pro-arrhytmic cardiac dysfunction related to beat-to-beat changes in the amplitude of intracellular calcium transient, that typically occurs at rapid pacing rates. Although oscillations in sarcoplasmic reticulum (SR) content have been related with calcium alternans, the experimental appearance of alternans without these oscillations suggests that another mechanism related with refractoriness of SR calcium release might be key, at least, under certain conditions. We investigate how RyR2 refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We find that a slow recovery from inactivation of the RyR2 might be crucial. On one hand, a steep relation between sarcoplasmic reticulum (SR) load and calcium release makes regular calcium cycling unstable at high SR calcium load and/or fast pacing rates, in agreement with previous explanation when RyR2 inactivation is not important. On the other hand, we show that calcium release can also depend strongly on the number of RyR2 ready to open if an important number of RyR2s inactivate after the release. This gives rise to a steep nonlinear relation between the calcium release and the level of recovered RyR2, so that a small change in the later produces big changes in calcium release. A conclusion of this result is that RyR2 refractoriness can be the main nonlinearity behind alternans even when alternation in SR-Ca load is present