I just checked: I looked at several messages that are sent as "multipart/alternative", and they all show in Aquamail just fine.
While I don't know the entire history (and I saw in the other thread where you posted that Kostya had looked at that OP's problem some 3 years ago), I wonder if in your case it is somehow due to your
HUGE size of the Aquamail database: 3.5GB is a lot for an Android device.
(And a pure speculation, but I suspect there could be some Android's internal problem with a database file approaching 3.5-4GB range due to addressing issues on a 32-bit system.)
If I were you and experienced this type of problems, I'd reduced the number of messages synced and cached, then compacted the database (that actually cleans the database from the messages that are
beyond the specified "window"), and tried to see if you still experience the problem you described.
Besides, I'd expect you'll get a significant performance boost for Aquamail.
Kostya, the app developer, when he gets to read this message upon his return (probably in a day or two?), will likely have an answer with a more technical details.
The question "How can I make a backup of my mail accounts?" is answered in the Aquamail FAQ:
http://www.aqua-mail.com/?page_id=227 .