On most nodes does “Continue on Fail” mean that it stops executing the node once an error occurs and proceeds with the next node. That has historical reasons that it does not continue with the other items. Changing that behavior for the Twitter-Node would be trivial but depending on what people currently are doing that could break their workflows. For that reason is the plan to go through all nodes and at some point and change it for all at once to make that behavior consistent and just have one version with that breaking change.
In the meantime should you have a look at this workflow. It shows how you can keep track of which tweets you did already process and so avoid this problem: