Hello EMSmac,
Thank you for using Apple Support Communities! I understand that you're experiencing an issue with the Mail app on both your iPhone running iOS 13.2 and iPad running iPadOS 13.2. I would be happy to help point you towards a resolution.
Since the issue doesn't appear to be isolated to a specific email account, I would like to have you go ahead and delete the Mail app from both devices, then redownload it again from the App Store:
Delete built-in Apple apps on your iOS 12, iOS 13, or iPadOS device or Apple Watch - Apple Support
Also, are any of the email accounts that you're experiencing the behavior with POP3 or are they IMAP? If you aren't sure, here's how to check:
If you can’t send or receive emails on your iPhone, iPad, or iPod touch - Apple Support
"To check if your email is a POP3 account, go to Settings > Passwords & Accounts, tap your account, tap Account, then look for the label POP Account Information. You can also check the recommended email settings for your POP3 email account in the Mail Settings Lookup tool."
In addition to the steps above, I'd like to collect a few more details if you're still experiencing the issue:
- Is this happening with email accounts from a specific email provider or multiple email providers?
- Do you use a VPN with either the iPhone, iPad, or both?
- Do you have a profile installed on either device under Settings > General > Profile?
Cheers!