The cross-blockchain transaction (CBT) serves as a cornerstone for the next-generation, blockchain-based data management systems. However, state-of-the-art CBT models do not address the effect of the possible local fork suspension that might invalidate the entire CBT. This paper takes an algebraic-topological approach to abstract the blockchains and their transactions into simplicial complexes and shows that CBTs cannot complete in either a \textit{committed} or an \textit{aborted} status by a $t$-resilient message-passing protocol. This result implies that a more sophisticated model is in need to support CBTs and, thus, sheds light on the future blockchain designs.