Does a rule chain break if one of the rules is broken?

I noticed some odd behavior on behalf of one of my customer's rule chains this morning. They had a chain of three rules that weren't dependent on one another and were scheduled to run on a daily basis. 

One of the rules in the chain stopped working altogether a few days ago due to a Salesforce permissions issue, so it failed right away. On the same day that rule failed, the rest of the rule chain stopped executing beyond that date as well, even though the other two rules were still executing successfully.

Is this expected behavior? If so, I would think this needs to be fixed.