I'm not sure how widespread this issue is, but I thought people should be aware of it. Apple support has confirmed this issue with me.
In rare instances, updating to El Capitan can cause aliases with iCloud email addresses to stop working in Mail. Since the Mac doesn't retain the aliases, the from popup menu will disappear. Attempting to manually enter the alias addresses in the accounts tab of mail preferences doesn't work, because the okay and cancel buttons won't work. Interestingly, I have two accounts on my computer. The aliases were not remembered in my primary account but worked in my secondary account.
While waiting for a response from Apple, I signed out of iCloud and deleted all of the iCloud services from my primary account. When I signed into iCloud again, it knew of my aliases and the from popup menu returned in new messages.
If you run into this issue, go to iCloud preferences, sign out, in each successive dialog, delete the iCloud services, and then sign into iCloud again. Note, you'll need to either know your iCloud four-digit security code or have another device that has been authenticated with your Apple ID to complete the sign in process. If you use another device, you'll have to enter that device's passcode and then your Apple ID password.
I hope no one else has to deal with this. If you do, this is the solution.