It sounds like one of the safety switches is bad.
If your furnace lights, but then goes off after a few minutes of operation, it sounds like your spill (rollout) switch, sail(air flow) switch, or high limit switch may be bad. These are thermal bimetal snap discs that look like this. This is not the switch for your furnace, it is just an example of what they look like.https://www.zoro.com/value-brand-set-limit-auto-reset-opens-200-468692/i/G4108027/?gclid=CjwKEAjwkq7GBRDun9iu2JjyhmsSJADHCD_HbMFQlYsmob8Xa_l4ZtxZ8hbCir6IxE4dQUJfzvqF2RoCs5zw_wcB
Each disc haS two spade terminals with slip on connectors. One at a time, remove the low voltage control wire from each side of the disc's spades and use a piece if wire to jump the two wires out. If the furnace fires and stays lit, then the problem was in the disc you removed. If it still goes out, move on to the next disc, and repeat the steps until you find the faulty disc. After the furnace has tried to relight three times, it will lock out. To rest, just turn off the red emergency shutoff switch, and turn it back on. This will unlock the control circuit. I can not stress this enough. DO NOT OPERATE THE FURNACE WITH THE SAFETY DEVICE JUMPED OUT. REPLACE IT IMMEDIATELY.
If your furnace has an induced draft, there is also a chance that you either have a weak pressure switch or there is an obstruction in your flue pipe. Both of these conditions would allow for an initial firing of the furnace, but could eventually cause one of the safety switches to overheat and cut off.
The pressure switch looks like a 2 to 2.5 inch flying saucer with hoses and wires going to it. If it has only two wires going to it, you can jump it out the same way you did the discs. If it has more than two wires or if you have to check the flue for obstructions, I suggest hiring a professional.