1985 Ford Bronco II, starts but gradually shuts off....
Fuel pump giving up the ghost would be my thoughts, harbor freight has a fuel pressure meter cheap that hooks up to your fuel rail and will tell you what kind of pressure you have or if the pressure regulator is bad,
Bad TFI Module. There was a big class action lawsuit and recall over it. The judgement came down in 2000 and it affected nearly every vehicle Ford made in the 80's and early 90's, including the Bronco II's. Your year is covered. If you have less than 100k miles you get a freebie, if not then they run $40-$90 at the parts store. Consider a custom mount location because even with a better design to fend off engine compartment heat, you are still mounting it right back into a hot box under the hood.
Oops my bad, your 1985 isn't covered so you'll have to buy one yourself. Only the 86-91 Ranger Bronco II 2.9L are covered. You still have a TFI on there.
Looking for a Used Bronco II in your area?
CarGurus has 26 nationwide Bronco II listings and the tools to find you a great deal.
Search Ford Bronco II Questions
Ford Bronco II Experts
Related Models For Sale