Ask Mr. Smarty Plants

Do you have deer in the area? This sounds more like deer "tasting" to see if they like it. Apparently they don't, if they don't eat the whole bloom.  Doesn't really make any difference, we truly have no magic wand to keep critters from grazing on your plants. The birds are probably not guilty in this case, as that is not their usual fare. Squirrels are generally more fond of large seeds (especially sunflower seed put out for the birds), nuts and grains.

We don't have woodchucks in Texas (or groundhogs, as they are sometimes called) so we had to go looking for information. The woodchuck is mostly herbivorous, primarily eating wild grasses, other vegetation, berries and agricultural crops. However, they also eat grubs, grasshoppers, insects and snails, which is beneficial to the gardener. Clearing of forests for urban development (like building your house, for instance) has provided them with more suitable habitat. 

Rabbits? Well, gee, what's not to like about little fluffy bunnies? Lots, we guess, as you'll see in this article from PennState Cooperative Extension, Monroe County, PA, by Laurel Bishow, Penn State Master Gardener, Rabbit Resistant Plants.

A very comprehensive article with lots of links is this one from About.com: Landscaping Organic Pest Control for Insect and Rodent Garden Pests. It also has information on repelling deer. 

Conclusion? We don't have any. We don't know what is eating your Gerbera jamesonii, which is, by the way non-native to North America, but rather to South America, Africa and Asia.  If that is the only thing that is being eaten, it may just be that they will have to be sacrificed. What lengths you go to, with traps, netting, sprays, etc., will depend more on how badly you want to keep those particular plants.