Morpheus' capture by Agents in The Matrix was a serious problem for Zion because hovership captains know the codes to the Zion mainframe. By interrogating Morpheus, the Agents could acquire the codes from him and access the Zion mainframe.
We later find out that the machines are capable of destroying Zion without access to the Zion mainframe, but Zion didn't know that. Zion was so concerned that the Agents would acquire the codes that some Zion operatives were willing to kill Morpheus to stop them. From Zion's point of view, Morpheus' capture meant not only the loss of one of their captains but a potential security breach.
Did the machines ever capture any other hovership captains, either before or after Morpheus? I'm aware of hovership crew members who were captured by Agents (e.g. Axel1), but the capture of crew members was not as serious to Zion since those operatives did not know the access codes to the Zion mainframe.
I am interested in the possible capture of any hovership captain, whether in the cycle of the Matrix depicted in the films (in which Neo is The One) or in previous cycles (in which one of Neo's predecessors was The One).
1Note that the Matrix Wiki article on Axel says that his captain, Soren, was also kidnapped; however, the Matrix Wiki article on Soren says that it was only Axel who was captured and that Soren helped rescue Axel. Furthermore, I didn't see Soren captured in videos of the Enter the Matrix mission in which Axel was rescued (see, e.g. Niobe's version and Ghost's version). Soren does not seem to have been captured, at least not during that incident.