Android - Persistent Notification for Calendar Events
I am replying (I see no one else has) because I have always used the calendar/notifications functionality in the EXACT same way you have, and was also distressed of this change in functionality. I think we are in the minority, though, because your post is the first acknowledgement I have even seen anywhere about this issue.
The only solution I have is to look at third-party apps. Although someone appears to have ported an older ICS/Jelly Bean-era version of the stock calendar which you can find in the Play Store, I have not used that too much. At the moment I am using Business Calendar, which I THINK comes somewhat close to replicating the functionality you and I are accustomed to (although I am still watching it to see). I also gave Today Calendar a very close look -- it is much closer to the Google aesthetic, and even has aspects of Material Design implemented. It appeared also to have persistent notification functionality, although for some reason I had problems with the syncing. This may have been fixed.
If you have come up with any solutions, I would love to hear them! Good luck!
UPDATE: 4 years later, I think Mike's comment is right, and I call on Google/Android to support a way to make a calendar reminder really persistent. I actually used the Calendar Snooze app for a while until it stopped being reliable. So I'm taking this comment back:
I initially had the same reaction you did about the change in Calendar behavior. But I just realized that a calendar is simply not the right app for these kinds of reminders that you want to persist.
In the meantime....
Instead of using the Calendar app for those sorts of reminders, you can use an app designed for reminders, like Google Keep , or Google Now, both of which have repeating reminder features.
If you say "OK, Google, remind me about the dance at 7 pm on Saturday" Google now will set up a reminder for you, which you can convert to a repeating reminder from the dialog box that pops up.
For tips on Google Keep, see Five Powerful Google Keep Features You're Not Using
And I hear that if you switch to the new "Inbox by Gmail" app, your Google Now reminders can show up in your calendar also. 5 reasons to switch to Inbox by Gmail, and 4 reasons not to | PCWorld
I found a workaround : delay the event in the future for x hours then add a notification x hours before the event. For example, delay the event to tomorrow and add a notification 24 hours before the event. The notification will stay in the notification bar until the event is ended. You can do the same with several days or one week if you want the notification to appear longer before disappearing.