Please post a picture of the timer/clock dials. Please try to incude a model number.

Model: BARE33009
Make: Admiral
Brand: Easy-Clean

You could have a timer that is shutting it off -- or you could have faulty electronics (switch or wiring). It could also be a safety feature that is shutting the stove off because it is sensing a circuit overload or some other fault. If you can rule out a timer being set, I would be inclined to replace. A new one would seem to be a huge upgrade and a lot safer (and better cooking) than faulty wiring. The oven insulation and cavity size are bound to be better -- though I will grant you the burners are remarkably level for that age.

If it worked before you started messing with the timers, then that may well be the issue. I had an old range with similar looking controls. The picture of the dials isn't large enough for me to read, but it looks like the two controls to the right of the clock are a start time and an end time. I suspect you've put the range into timer mode and the end timer is shutting it off immediately. I don't remember exactly how the settings work - you should try to locate a manual for your range if you can.

Does this help at all? I know there's not a great amount of detail but maybe you can figure out how to reset it to manual.

Here is a link that might be useful: Clock/timer on Admiral stove

I read ghostlyvision's link and tried out the suggestion around 2 weeks ago. I pushed in one of the buttons. I had already pushed in all of them, in every combination, at least 100 times, but this time it seemed to work and I have no idea why. 2 weeks of the stove working like it's supposed to. If it keeps working, I will never touch any of the buttons again. I can just use the clock on the tv or the computer instead.

The kitchen needs to be gutted. It makes no sense to bring in a brand new stove when I haven't even started gutting it (I have to live in this apartment for now) and haven't even started thinking about what to do with the kitchen. Otherwise I would consider buying a new stove. But this one works great, when it works.

I've got similar controls on my stove. I don't use them. But I've done the same thing in the past. The timers are in hours and match the actual clock hour hand. If you move them (I think the start time) off the actual time, the stove thinks you want to wait to start. Like if you want to start cooking something later in the day you would set the start time ahead and the end time even later. The oven wont come on until the start time.

I think.

Try cleaning. The control area with a vinegar solution. It might help or not but worth a try.
The appliance doctor radio show was always recommending this. I don't remember the concentration but try a 4/1 or 3/1 water to vinegar and heat in MW so hot but not boiling

Thanks for the update noah, glad to hear it's working for you. When we bought this house the p.o.'s left an older stove, I made a similar mistake trying to set the clock to the correct time and afterward the timer would ding every half hour or so. Fortunately they also left the manual for it so I could remedy that but it didn't take very long before we replaced that stove. lol

Yeah, so far so good I guess, except it started turning itself off again yesterday as I was cooking a pizza, while I was writing that post. So I left it in longer than it was supposed to be in there, and when I looked at it again, it was burned. Apparently it turned itself back on at some point. So I don't know what's going on. I did clean it, thoroughly, like a2gemini suggests, with vinegar and baking soda, before all of this, it's sparkling clean, and checked the fuses to see if they all had power (they do). I haven't been able to find a manual.