When the cursor disappears, that means the text area no longer has focus, and when you type, your keystrokes are probably going somewhere else, such as a dockable. To ensure that the keyboard is focused in the textarea, you can always use the mouse and click in it, but a more keyboard-friendly way is preferred when you are just about to start typing anyway. For this reason, a number of jEdit's actions have a side-effect of focusing on the text area as well.is one example. Some others are listed below:
In general, jEdit is a keyboard-friendly editor that is also mouse-friendly, so you should never be forced to use a mouse to do anything.