Each bird specie has different limits. Please see the table below:

Flippy Birds#

You can only buy 2 Flippy birds, total. Once you've bought up to 2, you can no longer buy additional Flippy birds, at all.

Frosty Birds#

You can only have 3 Frosty birds in your birdhouse at a time. When your Frosty birds die, you can buy more to replace them, but the most you can have in your birdhouse at any one time is 3.

Fruity Birds#

You can only have 2 Fruity birds in your birdhouse at a time. When your Fruity birds die, you can buy more to replace them, but the most you can have in your birdhouse at any one time is 2.