With an on premises system there is typically a single point of failure at multiple levels of the system. There is typically a single server hosting both the database and the software application. The software is usually accessed through a single network connection, single firewall, a single network switch and VPN.
With a web-enabled or hosted solution your software is also typically hosted on a single server. Because third party VPN or Citrix server is required for this solution, unless you are paying duplicate licensing fees, this introduces another point of break-down.
With a web-based solution there is redundancy at every step of the network and hosting process such that any single point of failure cannot bring down the system. Furthermore because of the multiple layers of redundancy designed to withstand a natural disaster it is very unlikely that you lose access to your software. Centrally managed servers enable this redundancy to the benefit of all clients accessing the software platform.