If you have a complex application with multiple moving parts you'd probably want to look into something like nagios.
Pingdom is pretty fail and unrealiable tbh. Hopefully this helps a bit.
However if you want to go a bit deeper and see how the underlying server is behaving you need something like http://servermonitoringhq.com
Pingdom - for global average responsiveness. Server Density - for server internals monitoring. Blamey & Stella - for public status reports.
I highly recommend checking out Blamey & Stella, if for no other reason than their brand is absolutely hilarious, and they offer a pretty good product, as well: