I just rebuilt a carb on my 89 corolla. When it does start it will idle up to 2000 rpms then shut off. What do I do the car sat for six years. So I rebuilt the carb. Before I did that it would start, idle up to 2000 rpms, bog down almost to where it would shut off then idle back up to 2000 rpms. It did this pattern about 15-16 times then shut off. Now after rebuilding the carb it starts hard, idles to 2000 rpms, and shuts off. Sometimes I can hold the gas pedal down and it sounds like it is struggling, let off the gas pedal then it idles fine but when I press the gas pedal again it just chokes out and cuts off.
Recheck your float hieght and whether the float actually floats or not. The alcohol in todays fuel may have eaten it up on the inside and it won't float any longer. Check for a vacuum leak after youget back running. Like a hose off or carb leaking at bottom.