Primarily since it's been an issue for over a year, reported here https://github.com/facebook/react-native/issues/8475 as well, with no help from the RN team.
> Also, that doesn't sound like a Babel issue, as I've compiled JS files that were several MB before without taking an unreasonable amount of time.
The error is specifically that transformation of the JS times out, so it very much appears to be a babel issue. It might be something specific to the RN preset though.
The "icebox" was automatic after a period of inactivity, if you are still having the problem, they give pretty explicit instructions on how to respond.
Also, that doesn't sound like a Babel issue, as I've compiled JS files that were several MB before without taking an unreasonable amount of time.