Do they show not installed in the Play store? Are they only gone on the screen, or are they missing in the app drawer, too? Is there any chance that you changed from one screen to the next (left/right swipe) without realizing it?
If they're GONE gone, maybe resetting the tablet, logging in with the same google account and starting over will help. But you can also look in the Play store, My Apps and you'll find a list of what is installed (under Installed) and previously installed plus what's there (under All) in that section. If you reset the tablet and started over using the exact same account will still show everything that was installed under the All tab. Depending on your settings, it may reinstall everything for you over time without you doing anything other than logging in with the same gmail account. (That's under Backup and Restore in Settings on mine. The specific item is Automatic Restore.)
I was considering getting an Ainol myself (the Nova 7). Not that I need one, but I like the name. I currently have a Hisense Vero 7 Pro that I really like. But the name is not as sexy.