I have what I think is the same issue. We had some items decorated with kendoTooltips which activated via showOn "click", and displayed some ajax-loaded content which included a hyperlink. With the default positioning, the content is directly below the item, and the natural reaction is to move the mouse down to click the hyperlink. This actually works some of the time, depending on the speed and care with which one moves the mouse; the rest of the time the tooltip disappears as one tries to enter it; it is possible that the ratio varies among OS and browser combinations. Here is a simple example.
I had thought that the tooltip content was intended to be entered, but was being flaky. But it sounds like the intent is actually that the tooltip should disappear as the mouse pointer leaves the parent area and enters the tooltip area? In that case, I assume that when it doesn't disappear, it is some sort of vagary in how "mouseout" and other events are being generated and handled by the browser and Kendo?
I'll look at the workaround above, but a built-in option to let tooltip content be considered part of the tooltip so that hyperlinks and other clickable content are usable in thise sort of case could be a welcome addition.