If something is fully asynchronous then it may never reach a decision.
It’s not exactly that but you’re close. We do have an issue with proving Liveness in an asynchronous setting because of a specific part of our algorithm: the concrete coin. It is not theoritically impossible to get liveness in an asynchronous setting. In fact, I am pretty convinced that when we get a bit of time away from the coding and look at the concrete coin again, we can create one that is strictly asynchronous.
The only reason we’re not alarmed about it and trying desperately to fix this part of the algorithm at the moment is because being strictly live in an asynchronous setting may not be necessary to be practically live in an asynchronous setting.
For instance HashGraph has a similar issue (actually, they’ve put less thought into fixing it than we have with our concrete coin, so theirs is more likely to be an issue in practice) but they haven’t bothered trying to address it because they don’t think it’s an issue.
Even the blockchain isn’t asynchronously live in theory, but it doesn’t prevent it from being useful without any use of time.