Well it depends on the solution you choose. It is possible to configure Nagios to do this, see here.

And I'm pretty sure that Big Brother can also be configured to warn/page only once per alert - but again, check the docs.

If you were just monitoring a single or a few processes and rolling your own simple monitor using Proc::ProcessTable, then it's just a matter of working out exactly what you want, and then defining a few rules. For example, you may set a flag once an alert goes off and a notification is sent, and then only reset the flag after either the alert goes away, or a certain time has elapsed. Writing a script should be the easy part - it's defining the business rules and getting them right that is the tricky bit :)

Cheers,
Darren :)