TJM5297, we want to ensure you don't miss out on any emails you receive. I'm here to assist. I just need a few more details. What type of email account do you have (yahoo, AOL, verizon.net etc)? Also, are you using the email application in your phone or the one from the email provider that's installed from the Play Store. Lastly, how much memory is available on your device under Settings>Storage?
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My apologies , I am going to muscle in with a similar issue that may apply. I had a Note 4 but am having the exact same problem on the Note 7 (question posted under the Note 7 forum).
My e-mail, using the pre-installed e-mail app, will download e-mail but larger messages only show the header information and I get the "Load More" button on the screen. Activating that button still fails to load the rest of the message. It either continues to process, bringing up the load more button again, or doesn't process at all.
My e-mail is a Verizon e-mail address but POP3 and IMAP servers are both Yahoo; if I go to either webmail the full message is displayed. The Note4 still had a little over 15 GB of memory available before I upgraded and the Note 7 has over 47 GB available.
I had responded back to this in the Note 7 forum but didn't think to update it here . I don't have the 4 on me, or the 7 either for that matter, so not sure of the exact sequence on the Note, however, if you go into the mail settings there is a selection that will give you the option of how big of a message you will allow to load. On my 7 Edge, I click on the e-mail app, select More on the top right, select Settings. Click on the e-mail address then about 8 lines down, you'll see "Limit retrieval size." If you select that, it will give you options for size of e-mail to download.
If the issue is your server settings, the settings would be the same as for your e-mail on your desktop, if you have one. Rather than try to explain it, it might be easier to go into a Verizon store and have them configure the settings if you aren't familiar with how that is done. It doesn't take long but it can be a little tricky.