Skype notifications disappear while there are unread messages, on iPhone I have an iPhone SE with iOS 13.2.2 and latest Skype.

Today I noticed, that notification about new messages in Skype are not shown on the lock screen.

What happened was that I has a chat with a contact, then I locked the phone and put it into my pocket. Then it vibrated once, and again later. I took the phone, turned on the screen and, there were no notifications shown.

I unlocked and there, there were new messages in Skype.

Then after a minute I locked the phone again, but now I held it in my hand, with screen on (but locked). Then after a while the phone vibrated again and a notification for Skype appeared but disappeared again immediately. This happened a few more times, for each incoming Skype message (all from same contact).

Is this some bug? Or setting? It worked fine before, even today.
Try going into your Skype settings (the settings app, not the Skype app) and scroll down until you see Skype, then click on Skype and check if Skype notifications are on.