2002 Toyota Echo stalling

I've been having serious reliability issues with my echo since the spring. The car periodically runs fine for 10-20 miles, then it misfires and loses power. First started happening late in the day on very hot days after running for a while being turned off and then started back up again (e.G. Running into the store). It will have power for 10-20 seconds, preferably in second gear. Third is less reliable. When this first happened it would start back up and run fine. Now it will cut out while I'm driving. The power cuts out but the engine doesn't stall out. It will have power then nothing, over and over again. If I park it it fixes itself. I've changed the clutch and the cat converter (was hoping it was backpressure). I've changed the ignition coils also, but they arent OE. When I have those few seconds of power and I'm trying to get home, it sounds like a lawnmower and is clearly not working on all cylinders. Performance has been progressively weaker for about eight months all the time. Last time it failed it had a very slight misfire right before the engine started playing the cat and mouse game.