I have a '89 Sentra that I use to get groceries and such. It starts
fine and seems like it runs pretty strong at first.

However, after about 10 to 15 minutes of driving/idling it stalls.
When I'm driving and I notice that it's about to stall, I give it more
gas and it doesn't seem to help. It's like the power is cutting out
making the car jerk for about a minute until it stalls. After
stalling, the car turns over and runs for a half a second and stalls
again.

Most times I'm already at the grocery store parking lot (my drive is
mostly downhill) when this happens, and when I come back to my car it
starts fine and goes back up the hill like nothing happened.

Any ideas? Thanks in advance!