Possibly the individual HTML files are too large.
Some older ereaders choke on them.
If you were to convert a book in calibre to EPUB, you would see a an option in EPUB Output to
"Split files larger than: ______" (default is 260 KB)
Performing an EPUB ==> EPUB conversion should fix that kind of issue, as would manually editing in the calibre Editor.
I would prefer the calibre editor, simply because conversions are lossy in regard to future-proofing, and calibre's automatic CSS flattening makes it harder to perform targeted edits later on.
In the Editor, right-click anywhere in the text and use "Split At Multiple Locations" -- it accepts XPath, you can split on header tags (header tags are usually used for chapter headers
which is a natural place to split) using the XPath Wizard.