See #1567 for pictures of the problem: under some circumstances we end up with parts of a longtable outside the typeblock, overlapping the bottom margin and sometimes flowing off the bottom of the page.

TeX is providing us with no warning or other indication that this is happening.

See this reduced example of sources triggering the problem:

My suspicion is that it's a bug in the longtable package.

The required setup for the problem appears to be a page that contains:

1. A table (in my case, at the top of the page, but I don't know whether that matters).
2. A longtable that entirely fits within the page.
3. Another longtable.

Under those circumstances, the permitted height of the second longtable before it first breaks to a new page appears to be miscomputed by an amount equal to the height of the floating table.