You haven't said whether your client is using Exchange, IMAP, POP3, or whatever, but I'm going to assume Not Exchange because you said PST (rather than OST). I'm also going to assume that your users are putting their PSTs in relatively normal places in their profile directories (which isn't necessarily a safe assumption).
I'm going to recommend something that backs up the user's profile data automatically, like Crashplan Pro or a competitor (Carbonite, etc.).
If you're talking about Exchange--and the Windows Server 2012 R2 and OWA tags make me wonder--you're going to want to back up the server instead. Any Exchange-aware backup software (including the free Windows Server Backup that came with your server) should do the trick.
If you absolutely insist on backing up PSTs and only PSTs, something like this might suit your needs.