Anyone who used Android knows that it does not, by default, repeat notifications for important events, such as missed called, text messages, email or calendar. One has to manually switch the screen on and look at the notification bar on the top to see what they missed. Ideally, Android needs to have a visual or audible notification that there is a notification that happened in the past.
Luckily there are many apps that provide this, and I review some that I have tried in the past, with the pros and cons for each.
By far, the best app that I used until recently was Light Flow Lite. I even paid for the full version Light Flow. It worked great on my Sony Ericsson Xperia Arc, as long as I was on GingerBread (Android 2.3).
It allowed me to assign to each type of notification a different LED light color and blink frequency, as well as a notification sound, vibrate and repeat pattern.
However, once I upgraded to Ice Cream Sandwich (Android 4.0), it stopped working completely, and all it did was drain the battery too quickly. It was no longer a viable option.
It seems that any app that wants to hook to Accessability in Android 4.0 would be a battery drain.
I then tried Droid Notify Lite. It provides a popup with contextually relevant buttons. I don't recall the specific issue that led me to uninstall it, whether it was user interface issues or battery drain.
Next, I tried LED Notify. Although this app was developed for LED-less phones that have AMOLED screens, so it can turn on specific pixels, rather than the entire screen, it does add several features that makes it a generally useful app for repeat notifications. Just make sure that you turn the screen flashing off if it eats up a lot of battery.
Tasker has the potential to be a very customizable solution for notifications, but it costs money and requires some time to develop the notification tasks. It also needs to hook into Accessability, and therefore potentially can be a battery drain.
Missed Message Flasher
My current working solution on Android 4.0 is to use Missed Message Flasher. This app tells you which notifications will need the Accessibility feature, which will probably drain your battery. This applies to Calendar, Email (not Gmail though), Skype and others.
I use this app to repeat notifications for Missed Calls and Text Messages only. I receive too much email via Gmail for it to be a distraction, and therefore don't have it turned on for that.
The app is configured to play a sound, which sadly is not unique for each notification type, but it does the job. It also is configured to vibrate.
The default "Timing and limits" settings are too frequent for my taste, so I changed them to start repeating every 30 seconds, and longer after that.
Thankfully, I don't use Email, just Gmail, and have a solution (mentioned below) for the Calendar).
For calendar notifications, Calendar Snooze does a good job to be able to repeat notifications and snooze events for later.
My final advice is to try out the above apps and see which ones work on your specific phone and for your specific needs. Post a comment below on what you find. Mention your phone make and model as well as the Android version that you are using.