Submit your application when it's 90% as good as it will be.

Well, the first thing I'd say is to work on your deployment model. While nothing is ever bullet-proof, you should definitely be ironing out deployment kinks before go-live anyway.

One of the things I've done in the past is standing up an additional VM to deploy things to -- sandbox changes occur on my PC alone, those changes are pushed to 'dev', wherein I ensure that the base functionality works. In the process of updating dev, I script or document every change that I had to make to migrate it to current -- I then test those scripts and procedures to the new instance ('qa') and run unit tests against them before believing that it will work in production.

Even still, you can't guarantee that production won't contain some data or user content that could break things, but it should at least get you more up to speed in double and triple checking your deployment strategies.

Another idea you might try is to just set up a 'stable' site on either another domain or sub-domain, and make absolutely sure that doesn't change (or at least doesn't change nearly as often) at something like stable.yourdomain.com, and point reviewers to that, with the advice that it may not be 'current'.

Post a notice on your site while you are updating the code and restore when done.