the ignition lock key switch is worn and has too much spring tension so, in fact, it is turning itself off when you release it while starting too quickly. If you release it slowly and it stays running, just don't release it quickly; if it sometimes turns off, try readjusting your ignition switch down on the underside of the column, if still having problems, replace the ignition switch.

You have a short or worn contact in the ignition switch seems to be the most probably issue.

I'd consider replacing it if it weren't for the fact it would probably cost more than the car is worth

It sounds like you need an ignition switch. Not a big job.

Sounds as though the key cylinder contacts are dirty or worn out .

bad starter?

I recently purchased a 1970 Ford Maverick, it runs great especially after I rebuilt the carb, put a new battery in it and fixed a hole in the exhaust. With all that being said when I start it I have to back the key off very, very slowly or it will die. It starts perfectly when I turn the key and it cranks, but if I just let go of the key it will die, whereas if I very slowly (over aprox 10-15 seconds) back it off it will stay running and then run all day if I need it to. What is going on here?