I drive a v-6, 96 Beretta. Your brief description sounds a similar to a gremlin that owned me most of last summer.
My car idled fine and cold, ran fine too. But after about 3-5 minutes, I'd give it a little throttle and it would stumble.
In some cases it would actually feel like the ignition cut out. If I pushed harder on the accelerator it would then accelerate
but it didn't seem to have normal power. I changed every sensor, TPS, MAP, MAF, IAT and coolant sensor. I changed ignition module, coils, plugs and wires. Tested fuel pressure and regulator. Even got a new EGR valve. I changed out the ECM too.
Finally, I read that spark knock sensors can become sensitive when they get old and that it could be retarding the timing when
it shouldn't be. I disconnected it and the car ran better. While it was disconnected, I did not push the car hard. So I got a new sensor and the car ran great. But after two weeks the problem came back. I got another sensor and it's been fine for months now. So you can try UN-plugging the sensor and take for a gentle drive, I.E. little or no boost. If it seems better, get a new sensor and try that. BTW, our 140k mile, 1985 HA still has the original knock sensor.