Plasma 5 makes a distinction between persistent and non-persistent notifications.
notify-send "Non-persistent notification"
sends a non-persistent notification, while
notify-send -t 0 "Persistent notification"
sends a persistent notification.
The different in behaviour (that I can see) is that non-persistent notifications disappear after a few seconds, and do not increment the notification count in the "Notifications" system tray icon. On the other hand, persistent notifications do increment the count, and (in principle) stick around until dismissed.
However, I have noticed that sometimes even persistent notifications mysteriously disappear. It happens intemittently, and on a timescale that seems to vary from ~20 minutes to several hours, but sometimes I'll come back to my computer after several hours of absence and a notification that should be there isn't. (I know it should be there because I had the application that sent it log that it did indeed send it.)
I assume this is a bug; it seems to me that persistent notifications should stick around indefinitely until they are dismissed.
Notifications of notify-send -t 0 command always disappears after ~5 sec
Notifications tray icon always displays 1 notification after multiple notify-send -t 0 commands
Operating System: KDE neon Developer Edition
KDE Plasma Version: 5.14.80
Qt Version: 5.11.1
KDE Frameworks Version: 5.51.0
Kernel Version: 4.15.0-34-generic
*** This bug has been marked as a duplicate of bug 390143 ***