How can I prevent an app being uninstalled from the Play Store?
One way to achieve what you want would include the following steps:


(temporarily) rooting the device
converting the app in question into a system app (e.g. using Titanium Backup ★ root, but there are also other apps helping you with this step)
unroot the device again


As the app now resides in read-only space (/system), the user cannot delete it without either rooting the device or flashing a ROM -- which of course could be done, but it's a higher inhibition threshold at least.