When you deploy an app through GPO, it leaves a "marker" in the registry to show that it doesn't need to re-install it. If you delete this marker from the registry and then gpupdate and reboot, it should deploy again:
See the following article for more details: ReInstall Applications Deployed Through Group Policy Software Installation - DeployHappiness
anectdotally, I've had to go one step further and go to the History section of that Group Policy branch, and in there you will find multiple entries that correspond to Reader or any other app you've deployed and I've had to delete those entries too to get an application to re-deploy.