The problem has been discovered during performance testing (see PERF-195)
TextInputControlSkin.caretTimeline timeline is never stopped (even when the text field is removed) and so (since it is an inner class) it holds the skin which in turn holds the text of the
text field and so we have both memory leak and (most likely) doing redundant work by updating caret for invisible text field.

I'd suggest to stop/start the timeline when the component become invisible/visible.