I have two groups and each group has a child element inside. Both child elements are connected using JsPlumb 5.12. When I click on the element and drag, the connections are broken.
For example. 'group1' has a child element 'elem1' and 'group2' has a child element 'elem2'. 'elem1' and 'elem2' are connected using JsPlumb connect method. when either of 'elem1' or 'elem2' is clicked and dragged, the connection lines are broken.
I saw the same issue in a demo which was part of JsPlumb doc. Has anyone faced this issue. How did u overcome this? I have attached the demo below.

As you can see when the child element of a group is dragged the connection is broken. It works fine when any other region of a group is dragged other than the child element.
Also is there a way to make a child element of a group not draggable?
If you think you have found a bug you'd be best off opening an issue on Github ( I refer to your statement "when the child element of a group is dragged the connection is broken" ).
Regarding switching off drag inside a group, there is a
setDraggable(el, state)method available on the jsPlumb instance which you could call to disable drag for some element.