You are not alone. I have been experiencing the same, extremely frustrating issue as well. I have three e-mail accounts configured within the stock e-mail client of my Samsung Galaxy S4 (AT&T): An Exchange account (for work), a Gmail account and a Hotmail account. I have also tried configuring only the Exchange account (to see if multiple addresses was causing the problem) but the same issue persists.
Description of Issue:
So basically, the problem is that every so often, when I press the e-mail button, all of my e-mail accounts are missing and I am then prompted to Set up an e-mail address (as if it's the first time I've ever pressed the e-mail icon).
I've owned the s4 for about a month and my e-mail accounts have "disappeared" 6 or 7 times. Every time, I have to set up my email accounts again like it's the first time. Additionally, my "disappearing email account" problem is not limited to reboots. If the phone is acting sluggish for any reason, I'm probably about to lose all of my e-mail accounts again.
PS - I don't want to use an alternate e-mail client. I like the stock app, but this is a major bug that I need to sort through.
Advice is appreciated!