When you get prizes and other things like that, they don't always have to come from the mini-games. Read the steps to find out what I mean.
Step 1: Go to the main menu and there you will see outing in the bottom right corner.
Step 2: Click on the bottom right corner where it says "Outing"
Step 3: You will be entered into a new menu where you have 5 options. (Connect, Open Cage, Change, Owner Info, And Credits)
Click on "Open Cage".
Step 4: A Question "Get it out of cage for a walk around room" will appear. Use you stylus and choose YES.
Step 5: Your Rabbit will appear in a different room. Sometimes you may see little gift boxes if you do look back at your menu on the second screen and use your stylus to choose HOLD.
Step 6: Use your arrows to control where you want to drop your pet. Be sure to drop it on the gift box.
Step 7: As soon as you drop your rabbit on the gift box wait, your rabbit will run into it. If your rabbit doesn't go to the menu and click HOLD again.
Step 8: Use the arrows to control where you want your pet. Go back the same gift box and be sure your rabbit runs into it, if not keep repeating this.
*HINT*: There are sometimes more then 1 gift box so keep looking because you can find some AMAZING prizes like a NEW CAGE :D