A lot of work has been done to model and analyze the performances of two-hop relay algorithm and its variants. However, the delivery ratio, especially under limited message lifetime, has been largely neglected in literature, which is not only of significant importance for delay sensitive applications (where a message beyond some delay limit will typically be dropped) but also of practical interests for general MANET scenarios (where mobile nodes are usually both energy-constrained and buffer storage-limited). In this paper, we study the delivery ratio of a generalized two-hop relay with limited message lifetime and redundancy. In particular, a finite-state absorbing Markov chain-based theoretical framework is first developed to model the complicated message delivery process under the considered relay algorithm. Closed-form expressions are then derived for the message delivery ratio under any given message lifetime, where the important interference, medium contention and traffic contention issues are carefully incorporated into analysis. Finally, extensive simulations are conducted to validate the theoretical framework and corresponding delivery ratio results.