'95 SVX fond of dying

[Shaboom]

I've got a '95 SVX that's been getting unreliable on hills. It used to just give me some engine shake when I got to the top, but lately it's escalated to sputtering and dying. It's worse if the engine's cold, but it'll still do it sometimes no matter how much I warm up the engine. Sometimes just getting up to freeway speeds puts enough stress on it to kill it. But the weird part is that after it dies and I restart it, it runs just fine. I can go up any hill, push the speed, etc.

My friend suggested that it might be a bad vacuum line and my mechanic said it might be the ECU, but he hasn't gone into it yet. Any ideas on what could make it do this? Winter's in full bloom and I'm in a hilly city. Thanks for any advice you guys have!