I have 2005 chevy aveo 4 door it is learching what could be the problem

Possibly a dirty or faulty mass airflow sensor. Check engine light may not come on while codes are pending, only when one is present so scan it to be sure.

This is a bad one, I have the same issue. I will tell you a mass air flow it is not it's impossible on this car. I did a complete timing belt kit on mine, cleaned the Throttle Body, TB position sensor, cold start solenoid, Replaced plugs, wires, cam position sensor, evap and purge solenoids to no avail. I did a smoke test, no leaks anywhere. I can purge the codes (they are meaningless on this car OBD2 doesn't seem to work on these) and it will run like a top for 10-15 minutes. Which leaves me to think it is the computer. The '09 beyond electrics are better and when I find a wrecked one, I will be adapting that computer.