Under corporate crises, the formation of credit relationships based on group-level credit reciprocity strategies is a multifactorial phenomenon. From the perspective of a fully mixed corporate group, the research explores the inadequacy of traditional snowdrift game models in adapting to the structural elements of credit relationship formation. Firstly, it improves the model by introducing inter-temporal costs, benefits, and crisis randomness of credit reciprocity as decision parameters. Secondly, it introduces inter-temporal credit reciprocity as a condition to allow the snowdrift game model to express the evolution between corporate groups. Finally, based on credit reciprocity, the mechanism of credit relationship formation is verified through numerical simulations. The results show that under the crisis probability, the formation of credit relationships exhibits a “threshold trigger,” and the inter-firm assistance and crisis probability play an important role in establishing credit relationships between enterprises.