According to this thread: https://github.com/blue-systems/plasma-5.4/issues/48
notifications are supposed to be marked as persistent or not by the developer (not by the user).

Nonpersistent SMS notifications are as useful as "you've got mail", because as soon as you click on the notification icon, you have one singe chance to read the message (if it's possible due to truncation of text as other bugs here describe). If you want to extract any text (mark and copy) you have to click "reply" to use the reply dialogue to do so (if it works), because it shows you the full original message.

This is one of the main features of kdeconnect for me: to be able to extract (i.e. mark and copy) text of SMS messages. In KDE/Plasma 4 this worked out of the box as all notifications were persistent per default. As this is changed in Plasma 5, I highly suggest to mark kdeconnect notifications as persistent - at least the SMS notifications or (the best solution!) make that configurable! Kind of notification => persistent yes/no. 
This is why we use Linux - we (the users) want to decide.

Kind regards and keep on the good job!

Reproducible: Always

Steps to Reproduce:
1. Receive SMS
2. Try to copy text to clipboard or read message a second time

Actual Results:  
Notification disappears

Expected Results:  
Keep notification persistent until dismissed

I'm using:
Kubuntu 16.04.1 LTS
kdeconnect:
  Installed:           (none)
kdeconnect-plasma:
  Installed:           0.9+git20160315-0ubuntu1