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Gravitational-wave detections are now probing the black hole (BH) massdistribution, including the predicted pair-instability mass gap. These datarequire robust quantitative predictions, which are challenging to obtain. Themost massive BH progenitors experience episodic mass ejections on timescalesshorter than the convective turn-over timescale. This invalidates thesteady-state assumption on which the classic mixing-length theory relies. Wecompare the final BH masses computed with two different versions of the stellarevolutionary code \texttt{MESA}: (i) using the default implementation of\cite{paxton:18} and (ii) solving an additional equation accounting for thetimescale for convective deceleration. In the second grid, where strongerconvection develops during the pulses and carries part of the energy, we findweaker pulses. This leads to lower amounts of mass being ejected and thushigher final BH masses of up to $\sim$\,$5\,M_\odot$. The differences are muchsmaller for the progenitors which determine the maximum mass of BHs below thegap. This prediction is robust at $M_{\rm BH, max}\simeq 48\,M_\odot$, at leastwithin the idealized context of this study. This is an encouraging indicationthat current models are robust enough for comparison with the present-daygravitational-wave detections. However, the large differences betweenindividual models emphasize the importance of improving the treatment ofconvection in stellar models, especially in the light of the data anticipatedfrom the third generation of gravitational wave detectors.

Sensitivity of the lower-edge of the pair instability black hole mass gap to the treatment of time dependent convection