We've actually had less broken downtime since we started doing automated deploys than we did beforehand. It's partially the result of good testing, partially because the changes are just so much smaller than they used to be, and partially because pushing to our master git branch is now serious business.
If you only deploy in big steps, you have already worked on a few other things and have forgotten a lot about the (broken) code. So fixing things take more time and it becomes more difficult to learn the 5 whys behind the bug.
Continuous deployments ensure delivery of features and turn around time fast enough for a changing business model of startup and can't be stopped either.
So uptime and continuous deployment model has to happen at the same time.
Deployments should always be automated and revertable. If you think you can run a healthy startup with just about adequate mistakes perhaps you got an easier place to work at :)