This problem seems to happen when the search query (that triggers Quick Answer by ending with '?') is long.
Writing a followup question does not send you to the thread page containing the initial query and the follow up, but instead, sends you to a 404 page.
Here is a specific real example:
Search query: generic term for (typically) rubber material thing that connects rotary motion of one part of the car engine with other parts?

After submitting the followup question, we get a 404 and a defunct URL:

Even if I check my assistant.kagi.com Threads, it is not there either.
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I expect it to work normally as expected.