I'm not sure if this is a bug or a design limitation I'm unaware of.
Last night, my daughter attempted to send me a video clip of my grandchildren. It was a short clip, about 5 MB. It was sent to my live.com account, but I wasn't seeing it in AM. Instead, I was getting "persistent network error". I kept trying for a while, with no success. Then I installed MailWise and added the live.com account, and it came through instantly, with no network error. The email still wasn't getting through to AM.
I kept MailWise on my phone (a OnePlus One running CyanogenMod 12.1) and this morning tried a test. I mailed another attachment, 7.5 MB, to the live.com account. Once again, AM is giving me "persistent network error" but MailWise got the email with the attachment. It got to MailWise at 8:15 this morning. It's now 8:35 and still not in my AM inbox, despite a 15-minute sync setting and numerous attempts to refresh manually.
Also, to continue the test, I sent another email from the same (Yahoo) account to the live.com account, this time with just a few words and no attachment. This one appeared immediately in MailWise, but still isn't in AM. Instead I got the error "Mail folder is missing on the server." Also, AM tells me there are three unread mails in my live.com inbox, but there's only one (a separate issue, but I thought I'd mention it since it could be related).
And I've just noticed another email has arrived in my live.com inbox on MailWise -- a notification from my bank -- but I can't get it to appear in AM. It's as if the email with the attachment has broken the connection to the live.com account, if that makes any sense.