so I've got a 1990 xj with the I6 and automatic transmission. Yesterday, I drove about 15 into town and parked it. On the way, first my stereo died, but the Jeep was still running, so I pulled over, shut it off, fired it back up and it ran perfect. Well, along the way, then I lost my turn signals. Well i got to my destination. I went in and talked for about 20 minutes, came back out and I had electrical power and everything, but it wouldn't crank at all. Well, about an hour later, it cranked and fired up, but it was slow. I was watching my volt gauge and it was going down, so I figured I lost my alternator. Well, I towed it home and replaced the alternator and charged the battery for a couple hours. I was on my way to school this morning and it died again, and same thing at the place yesterday, I had lights and everything but no cranking, after like 7 minutes, I fired back up, barely, and I limped it in. On my way to lunch, the thing died again, fired it back up barely and it ran. Got to lunch, came back out and it fired right up. But on my way back it died again, and I needed my buddy to jump it to get it back up and going again. It seems to run when I bump it up above idle rpm. My dad thinks it could be the ignition switch, but does anyone have any other ideas?

Any help would be great,
Thanks!