We use Microsoft Outlook and Exchange at my company, and almost nothing is stored locally. Even draft emails are stored on a server that is backed up every night. That storage is also mirrored, which means that each piece of information is stored twice so that it can be recovered in the event of a hardware failure. The server is backed up every night with the backup media being shipped offsite each day by an outside vendor that specializes in data backups and security. So if our data center was destroyed by fire, the backups from the previous day could be restored to a temporary data center and I would have access to my email within a couple of hours. In essence, I would lose a maximum of 24 hours of emails. And if I sent any emails outside of my own network, there's a chance that they could be recovered at the other end. It is a very strong strategy that almost every single company employs.
However, I once managed to lose three emails through no fault of my own. My desktop software was upgraded, which caused a rare conflict with Outlook. Strangely, it was a display driver problem at the root. I had sent three emails that afternoon and just assumed that they had reached their intended recipients inside the company network. That evening, I noticed that they were sitting in my outbox. I tried to resend them without success. So I figured I'd close Outlook and try again. If that didn't work I would restart my computer before calling the Help Desk as my last resort. But alas, when I reopened Outlook, the emails were gone. They were no longer in my outbox and did not exist in my drafts folder. Tech support told me that I should have moved them to my drafts folder or copied the contents to a Word document or Notepad before closing Outlook.
So you see, it is possible to lose emails, even in the 21st century.