In several programs I've used, the cursor stops blinking after the user has not interacted with the program for several seconds. gnome-terminal and gedit both do this, and I can't find any reasoning about why this happens.
I would assume that the cursor blinking is useful, as it draws the eye to where text will be inserted, so I don't understand why it would be good design for the cursor to ever stop blinking. Assuming the user has looked away from the screen for a moment, surely the cursor stopping blinking would just make it harder for the user to find the cursor again?