I assume you are using the caption feature of Word, that is, captions were not typed in as normal text, but were inserted using Insert > Caption (Word versions before 2007), or References > Insert Caption (in the ribbon of Word 2007 and up). If done correctly, the captions are really 'fields'. You'll know if it is a field if the caption's background turns grey when you put your cursor on them (or is permanently displayed grey).
Captions are fields - Unfortunately fields (like caption fields) are only updated on specific actions, like opening of the document, printing, switching from print view to normal view, etc. The easiest way to force updating of all (caption) fields when you want it is by doing the following:
Captions are normal text - If the caption number is not a field, I am afraid you'll have to edit the text manually.