This can be an issue, I do get lazy about checking them when I'm busy.
The next step will be to automate checking them a bit more, rather than stopping the positive messages. A simple script that for the mail example logs in via POP/IMAP, checks for the last notification and checks the relevant timestamps. Similar for other services (is the last commit in the repo from more than 24 hours ago?). Then I get a simple "all OK" or not. I still have to run the script, perhaps hooking it to CGI and setting it to my browser home page to further remove my laziness from the equation, but I don't want to just be told when something is wrong as I'll never really trust that something going wrong won't block warning messages - I want to make checking as easy as possible though.
I may play with your service and add it as a secondary set of checks though!
This is sensible, but one problem with this is developing "blindness" for messages you receive every day. For some recurring tasks you can automate a bit further. Instead of receiving a success message every day, receive a failure message the first day there's an absence of success message. A number of tools and services exist for setting this up, one is linked in my HN profile (shameless plug ;-)