Type about:config<Enter> in the address bar. If a warning screen comes up, press the Be Careful button. This is where Firefox finds information it needs to run. At the top of the screen is a search bar. Type; privacy.clearOnShutdown.downloads Set its value to false.

Changing that pref won't work because Firefox will likely give it the same value as privacy.clearOnShutdown.history.

You can check the "Clear history when Firefox closes" settings in:

• Tools > Options > Privacy > Firefox will: "Use custom settings for history"

Thanks FredMcD and cor-el, The first suggestion did not work for me but cor-el's did work. Thank you both for your input.