The reason they are disappearing is because the Paragraph style isn't the same as a character style, so it treats this text as locally formatted, meaning being applied without a style. It just thinks you really don't want to apply the bold and italic. It's a bit crap really. But if you serach for a plug in called Preserve Local Formating. It's a script, you can select all your text and run this script, it will create character styles for you, bold, italic, bold italic, superscript, subscript etc. All in one go.
You could make these styles yourself and find replace Bold in the text to the Bold character style, and the same with italic, bold italic etc. but it can get a bit messy.
Trust me, creating character styles is a massive help if or when you have redo a job. I have 3,200 page book at the moment that needs to have the new additions in Bold. I have a special character style set up for this, because if they want to change that bold to Italic or Bold Italic, I can change it in a few clicks throughout the whole book.