On this occasion, people are not just losing valuable play time, some also report the loss of permadeath Hardcore Mode characters to the error.
In response to the complainants a community manager offered the following explanation:
We’re currently working on a fix for this and are looking to have it implemented as soon as possible; we hope to have future patching processes smoothed out for Diablo 3.”
The patch in question, update 1.0.2, is mostly for bug fixes including login error 14009.
Sadly, I suspect this is not the last we will be hearing of Error 37.