We'd like the option for alerts to repeat until an issue is resolved. For instance, we may have a custom alert to tell us when a DBCC CheckDB hasn't been performed in >24hrs. For that we'd perform the check once per day and expect to get an alert every day that the problem continues. Without the alert recurring it's very easy for it to slip through the cracks and get missed.

Another example is blocking. We have some databases where we monitor blocking via SQL Agent and when a block occurrs for 1m or more, we send emails every 30s to the application owner so they can address the issue. This is intentionally annoying and intended to get the attention of someone who may be working on something else.