Hi @kaa2020 DSS will reuse (unless otherwise told) the existing training and test data split, but the models will be built from scratch each time.
Re system being unstable, this is indeed something you should investigate. Consider training a model at a time or with fewer hyperparameters, to reduce training time. This is not ideal since you'd then need to compare across multiple training sessions but it might be a way to get some models trained before the system crashes again.
I hope this helps!