After instaling Caffe whenever you want to update homebrew, switch back to the master branches, do the update, rebase the caffe branches onto master and fix any conflicts.

brew-update-w-caffe-branch-OSX.sh

# Switch batch to homebrew master branches
cd /usr/local
git checkout master
cd /usr/local/Library/Taps/homebrew/homebrew-science
git checkout master

# Update homebrew; hopefully this works without errors!
brew update

# Switch back to the caffe branches with the formulae that you modified earlier
cd /usr/local
git rebase master caffe
# Fix any merge conflicts and commit to caffe branch
cd /usr/local/Library/Taps/homebrew/homebrew-science
git rebase master caffe
# Fix any merge conflicts and commit to caffe branch

# Done!