No fire to fuel pump

Hello and welcome to 2CarPros.

Is the service engine light on? If so, get it scanned by a mechanic's shop. If not, then it sounds like the fuel pump is losing pressure as it warms up, which is a fairly common occurrence in older fuel pumps. I would suggest checking the fuel pressure by borrowing a fuel pressure gauge from the local parts shop and hooking it up to the valve under the hood. Here's our general guide on that:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

The information that AllData has on checking this car's fuel pressure is included in the images below.

I'm also going to look up the fuel filter and post the relevant information in another response below, as it's a possibility, although I'm leaning towards the pump itself. You'd want to put a new filter in with a new pump anyways, so you might as well try it before putting in the pump.

Here's the information on the filter. It's entirely possible that the filter is clogged to a point where it'll still run for a bit, but eventually backs up the system enough that the engine is starved for fuel, and the car stalls. Again, this is less likely, but possible.