currently kdeconnect displays sms or any other notifications only once and it doesen't even persist in the kdeconnect applet in the taskbar. Either allow messages and alerts to persist in kdeconnect under applicable paired device or log them to systemtray notifications so at least the sms messages can be read.
Normal notifications from your phone should persist in the KDE Connect applet, even after the bubble disappears. SMS notifications (the ones displaying a "reply" button) don't, but these should remain available in the normal notification system tray. Note that (by default) you get two notifications for an SMS message: a "normal" one, and one specific to SMS messages. As I read your report, you're talking about the first case (normal notifications, including "normal" SMS notifications), and they do not persist in the KDE Connect applet. Do I understand you correctly?
Yea normal sms, and iirc reply button is only avialable to notification popup.
Fixed in 1.3