"Execute Code First Migrations" checkbox disappeared from my publish profile

Here is the right answer - is solved the problem for me. Just rename your connection string exactly as your DbContext, e.g.

        public ApplicationDbContext()
        : base("Vocabulary.Domain.ApplicationDbContext", throwIfV1Schema: false)
    {
    }

Note that name should include namespace like "Vocabulary.Domain.ApplicationDbContext". Don't forget to update .pubxml files:

    <ObjectGroup Name="Vocabulary.Domain.ApplicationDbContext" Order="1" Enabled="True">

This article describes when publish dialog has or has no the tick "Execute Code First Migrations (runs on application start)"

Since asking this question, I've run into this problem several more times in multiple versions of MVC and EF (all code first though of cource). When it happens, don't save the changes to your publish profile, make sure you are on the 'debug' build configuration, clean solution and rebuild solution. And if all that fails, restart Visual Studio and try again. So far, this has always solved the problem for me.