I've had this same problem. I have a 3rd generation Apple TV and an iPad Air which hasn't been able to display the keyboard when using the Remote App on IOS7. I tried the following...
1. Delete the Remote App from the iPad
2. Restart the iPad
3. Reinstall the Remote App - No keyboard
4. Reset the iPad's network settings - No keyboard
5. Backed up the iPad
6. Erased all content and settings from iPad
7. Setup as new iPad
8. Installed Remote App - Success! Keyboard now displays
9. Erased all content and settings from iPad
10. Restored iPad from Backup taken in step 5 - Success! Keyboard still displays
I'm still unsure what caused the problem as my iPad is theoretically exactly the same as it was when the keyboard wasn't being displayed because I've restored it from a backup taken when the problem was there.
I'm just glad I can now control my Apple TV again without having to manually type with the standard Apple remote control.