Thanks for writing. This, as you've discovered, is a very tough problem because rats are very intelligent and determined.
The best advice I've heard is to make the area as unfriendly to rats as possible: Clean up any debris areas, put woodpiles on legs so they're above the ground, and eliminate any areas from your yard where the rats may be living.
There are a variety of deterrents such as Shake-Away or Animal Stopper that you can try using. They have varying degrees of effectiveness.
If you have a spot where you can grow your tomatoes in hanging baskets, that may also offer a solution because the tomatoes will be very difficult for the rats to get to.
If your community allows for it, you might consider trapping or baiting the rats --- but rules about this vary from community to community. And there's no garauntee that new rats won't find your tomatoes.
Senior Garden Editor, BHG.com
Better Homes and Gardens
Other than that, I'm afraid I have no other solutions. This is one of those situations where there's no magic answer.