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Lets try the following steps, which even though it will temporarily delete the verizon account from your ipad, this wont delete your mail stored in verizon itself.
Go to home screen, then settings, then mail, then remove your verizon account.
Then, follow these steps to reset the network settings on your ipad.
Once reset.. turn your ipad off, t hen back on. And then connect it to your wireless network again.
Now, the last step is to add your verizon email account to the ipad again.. This should help.
That should do it.. You should be able to both receive, and send mail again. let me know if you have further questions or run into any issues completing these steps.
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Senior Technician and Network Switching Systems Operator / Maintainer.