  Dynamically available total-order broadcast (TOB) protocols tolerate
fluctuating participation, e.g., as high as 99% of their participants going
offline, which is especially useful in permissionless blockchain environments.
However, dynamically available TOB protocols are synchronous protocols, and
they lose their safety guarantees during periods of asynchrony. This is a major
issue in practice.
  In this paper, we propose a simple but effective mechanism for tolerating
bounded periods of asynchrony in dynamically available TOB protocols that
ensure safety deterministically. We propose to trade off assumptions limiting
the online/offline churn rate in exchange for tolerating bounded asynchronous
periods through the use of a configurable message-expiration period.
  In practice, this allows picking a small synchrony bound $\delta$, and
therefore obtain a fast protocol in the common case, knowing that the protocol
tolerates occasional periods of duration at most $\pi>\delta$ during which the
bound does not hold. We show how to apply this idea to a state-of-the-art
protocol to make it tolerate bounded periods of asynchrony.
