How frequently is Photo Stream synced to Aperture?
Normally Photo Stream should sync across devices within seconds, so long as the device that took the photo is on WiFi. However, I've also run into cases where Aperture's PhotoStream folder lags in showing recent images. When this happens I've been able to fix the issue by disabling and then re-enabling Photo Stream in Aperture's settings. It will re-sync everything in the Photo Stream folder, and new pictures show up almost instantly.

Hope this helps.