Hi Pertinax, I've been able to locate the examples where this is an issue for you by looking directly in the database - but I can't reproduce this behaviour myself.
Basically what you're ending up with is a quote within a quote.
So you quote someone else's message and both the quote and your reply get wrapped inside another quote, so it gets hidden in the "quote" box (it is actually there) rather than displayed normally.
I'm wondering if you're clicking the "quote" button in the toolbar to add those quotes? You shouldn't need to do that - just hitting "Reply" on the message you want to quote will insert the quotes automatically.
Only use the "quote" button when you're quoting some external source rather than a participant in the conversation.
... do don't use the Quote menu option in the screenshot above for when replying to someone in your conversation.
Also, if you're typing out a reply, make sure you start typing it
after the [/QUOTE] at the end of the part you're quoting.
I hope this helps.