No you will not have to set up the iPad all over again. Resetting the iPad is like rebooting your computer. You will lose no apps, data, settings .... Nothing at all. I like to use the expression that it's like "clearing out the cobwebs" on the iPad's memory.
The reason I am suggesting this is that there are some other sort of bizarre issues that occur in the mail app and the reset seems to clear up those issues. So I think it is worth a try.
On the other hand, if you have restored the iPad to factory settings, I don't know that it will help. If nothing else works, try going to your web mail using a browser and see if you can't deal with this in there.