A persistent problem with sending emails on an iPad could be caused by a lack of connectivity on the device, a problem with your email client or an issue with your email provider's server. Troubleshoot each of these potential problems in turn to pinpoint and resolve the issue.
Check your iPad has a working connection to the Web by launching Safari or an alternative browser and visiting a handful of sites on the Internet. If pages do not load, you need to find a working Wi-Fi or data connection before you'll be able to send emails successfully. Ensure the "Wi-Fi" or "Cellular Data" option is switched on in the "Settings" app so a connection can be established. Accessing the same Wi-Fi or data connection using a laptop or mobile can help establish if the connection itself is at fault.
Check the email configuration settings in your client app to ensure everything is set up correctly, particularly the outgoing mail server (SMTP) details found in the "Accounts" section of the "Mail, Contacts, Calendars" page in "Settings." If you're using an app other than your iPad's inbuilt email client, uninstalling and then reinstalling it again may be enough to resolve any temporary bugs, enabling you to start the configuration process again from the beginning. Check with your email provider for the correct SMTP details.
It's possible that your email provider is suffering an outage preventing you from sending emails successfully. If this is the case, details should be posted on your provider's website or Twitter feed, or in the case of larger services like Gmail, in the technology press. Some email providers have a specific service status page on the Web you can visit to check for any recent problems.
If a temporary error or conflicting app is interfering with your iPad's email functionality, restarting your device should be enough to resolve this. Press and hold the "Sleep/Wake" button then drag across the red slider to power down your tablet. Press and hold the "Sleep/Wake" button again to turn it back on. Deleting and restoring the relevant email account under the "Mail, Contacts, Calendars" heading in the "Settings" app may also resolve issues with sending email.