Can I temporarily stop update notifications for one project only?
See Update Advanced module:


  Extends the administrative interface for Drupal core's "Update status"
  module. In particular, the per-project settings to ignore certain
  projects or even specific releases, is absent in the core version of
  the module. The "Update status advanced settings" module restores
  these settings, and might eventually provide additional functionality
  for the core "Update status" module.