1. Ensure your app updates are complete (open the store, click on the picture next to the search (upper right side), click on downloads and updates).
2. Any other issues? Perhaps consider refreshing your install, which acts like a clean install, so think and consider before you do this step.
3. What happens when you open the emails in Outlook.com? Do they show up there? Are they unsupported attachments? Send something like a picture to yourself to verify.
4. What mail account is this? If it's Google/Yahoo/AOL/etc. Is that company preventing the attachments from making it's way through (yes, a weird thing to say...BUT, it wasn't long ago I confirmed both Yahoo and AOL wouldn't work on a Windows phone email program because they wanted you to purchase their own software (true story...I found this out as I was helping a priest set up his Windows Phone). Anyway, I added Google to this as they play dirty pool and definitely don't play well with others.