In clinical trials, covariate-adaptive randomization aims to achieve balanced allocation of treatment groups in terms of assignments and known covariates. However, in real-world settings, some relevant covariates may be unobserved, leading to imbalance and consequently loss of inferential precision. This study quantifies the impact of unobserved covariates on the performance of the recently proposed Simulated Annealing Design. Considering various experimental scenarios, the results show a substantial loss of information when one ore more factors are omitted from the randomization procedure. Additionally, we investigate the effect of discretizing continuous covariates, highlighting the importance of accounting for all relevant factors and preserving their continuous nature to guarantee reliable inferential results.