One of the largest obstacles that keep people from making the "digital jump" is their fear of the well-known computer crash that erases all of your records and puts a halt to your life while you try and salvage what you can. Even for clients, the inherent distrust of technology can inhibit their ability to understand and appreciate the lengths at which technology allows you to beat out all other competition.
In order to put away those fears and fully release yourself in the digital era, you need to have backup systems in place, both for you and your clients' sake. The most effective way to do this is online, whereby you can hire-out the storage space and time that it takes to manually backup files that come into your system each day. There are companies today that will even scan and backup paper files on their own servers, which removes even another hassle. Some of these backup companies also have internet access, whereby you can access their servers (with your data) on a daily basis.
Making the investment in data backup is necessary for the security of your entire business. To allow your firm to work off of one copy of all client data puts you in a very hazardous position, and will have your firm in dire straits when your server fails. Seek out those companies that will backup your data as often as you update it, because it will not only eliminate that risk of data loss, but it will also allow you to answer your clients' question of data security with one simple explanation.