I believe you may have the same issue I had. Go to each email account if you have multiple. Go to setting > send & receive > Download Options. I may be wrong but I noticed that if the download days wasn't set to 'ALL' it would remove emails that were older then 3, 7, 14...etc days. So if you had this setting on 3 days after that email was sent 4 days ago it would remove it from your phone. Ultimately I set it to 'ALL' and have not had an issue. Keep in mind that once you make the change it will re-download all of your emails that are on the server. You may have to delete a bunch of emails you no longer need. Let me know if this helps.