birds and tomatoes... I'm sure to get flamed for this.. but birds don't want your maters.. they want the liquid.... so try this... put out a few plates of water for em and they will leave your mater alone. and maybe they will pay you back with eating a few bugs.
Hmmmm, no flaming from me but I dunno ... I have a big bucket of water out for the dog (that I've seen the birds in), a pail out for the chickens (that I've seen the birds in) and a bowl of water for the feral cat that hangs out in my backyard (that I've seen the birds in) ...
I don't think it's the water they are after ... That said, it could be the squirrels snagging them but I can't imagine squirrels would like green tomatoes very much ...I do smell a skunk odor back there every once in a while. And a neighbor has told me that we have a raccoon who climbs our fence but I dunno about either of those either because it seems to me they'd be trying to get the chickens and the rabbits if they were getting in MY backyard instead of another neighbors ... And we are never missing any eggs ...
Hmmmm ... I'm gonna ponder this some more ...
HI CLOCK! 
I caught my danged dog eating my tomatoes right off the vine. She did the same with the strawberries and I caught her pulling potatoes and eating them! She just loooooovves to help me garden.
HiyasHI CLOCK!
The wife and I was out picking some more tomatoes this evening and finally got around to measuring how far the two plants had spread. 14 feet long by 11 feet wide so far. Still producing too. 
