You don't need to stop the capture and run aircrack after. You can run aircrack-ng while doing the capture, and it will keep trying to crack while the IVS count is rising. That way you don't need to wait to reach thousand of packets, aircrack-ng will just warn you (and by warn, I mean show you the WEP key) once it finishes cracking.
Check if the fake authentication was successful and make sure the data packets are being produced thanks to your attack and not due to someone in your network using torrents/streaming apps/et al. To finish, make sure you are using tutorials from aircrack's website, they are the best.