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First-generation blockchains provide probabilistic finality: a block can be revoked, albeit the probability decreases as the block "sinks" deeper into the chain. Recent proposals revisited committee-based BFT consensus to provide deterministic finality: as soon as a block is validated, it is never revoked. A distinguishing characteristic of these second-generation blockchains over classical BFT protocols is that committees change over time as the participation and the blockchain state evolve. In this paper, we push forward in this direction by proposing a formalization of the Dynamic Repeated Consensus problem and by providing generic procedures to solve it in the context of blockchains. Our approach is modular in that one can plug in different synchronizers and single-shot consensus. To offer a complete solution, we provide a concrete instantiation, called {{Tenderbake}}, and present a blockchain synchronizer and a single-shot consensus algorithm, working in a Byzantine and partially synchronous system model with eventually synchronous clocks. In contrast to recent proposals, our methodology is driven by the need to bound the message buffers. This is essential in preventing spamming and run-time memory errors. Moreover, {{Tenderbake}} processes can synchronize with each other without exchanging messages, leveraging instead the information stored in the blockchain.