  Context: Thermal non-equilibrium (TNE) produces several observables that can
be used to constrain the spatial and temporal distribution of solar coronal
heating. Its manifestations include prominence formation, coronal rain, and
long-period intensity pulsations in coronal loops. The recent observation of
abundant periodic coronal rain associated with intensity pulsations by
Auch\`ere et al. allows to unify these two phenomena as the result of TNE
condensation and evaporation cycles. On the other hand, many intensity
pulsation events observed by Froment et al. show little to no coronal rain
formation. Aims: Our goal is to understand why some TNE cycles produce such
abundant coronal rain, while others produce little to no rain. Methods: We
reconstruct the geometry of the event reported by Auch\`ere et al., using
images from STEREO/SECCHI/EUVI and magnetograms from SDO/HMI. We then perform
1D hydrodynamic simulations of this event, for different heating parameters and
variations of the loop geometry (9000 simulations in total). We compare the
resulting behaviour to simulations of TNE cycles by Froment et al. that do not
produce coronal rain. Results: Our simulations show that both prominences and
TNE cycles (with and without coronal rain) can form within the same magnetic
structure. We show that the formation of coronal rain during TNE cycles depends
on the asymmetry of the loop and of the heating. Asymmetric loops are overall
less likely to produce coronal rain, regardless of the heating. In symmetric
loops, coronal rain forms when the heating is also symmetric. In asymmetric
loops, rain forms only when the heating compensates the asymmetry.
