It is virtually impossible for Juni to get killed outside a story mission; even inside story missions it is very unlikely that she gets killed because her ship is indestructible most of the time (probably the result of Microsoft QA). Good thing too, for when I destroyed the two killable cruisers near Benford in mission 4 I tried to hasten the process by dropping homing mines at my prey and it took half a dozen mines or more for me to notice that Juni was nearer to my ship than the cruiser I was working on, and that all the mines were hitting her ship.
There are only two occasions where a dialog pops up during a random mission that I can think of. First, some bystanders scan your cargo hold and express desire for the contents. Not very likely, but not impossible either. Second, you had a 'capture' mission but your prey was destroyed by gun fire or environmental hazards (mines, radiation) before you tractored their escape pod; similar things could happen on a 'tractor stuff' mission.
Have you visited Tobias at the equipment dealership in Leeds before venturing out after mission 4? What is your current level and net worth, and what is the entry for 'Next Level Requirement'?
If you have met the conditions for the next story mission then usually the path to where Juni awaits you gets highlighted on the nav map, whenever there are no waypoints that you have set manually or that are the result of booking a random mission. However, it seems that the automatic 'path to Juni' feature does not always have infinite patience - in very rare cases it can give you up for hopeless if you ignore it for hours and days on end.