Does iPhoto need to be open in order to download Photo Stream photos? Apple's official documentation on Photo Stream states:


  My Photo Stream stores the last 30 days of photos taken with your iOS
  device or imported from a camera to your Mac or Windows computer, and
  automatically pushes them over any available Wi-Fi or Ethernet
  connection to each of the devices that you set up to work with iCloud.
  
  For example, if you take a photo on your iPhone (or save one to your
  Camera Roll), iCloud automatically stores the photo and pushes it to
  Photo Stream on your iPad, iPod touch, and other Mac or Windows
  computers.


What's not clear to me is this: does iPhoto actually have to be open in order for Photo Stream photos to be pulled down to my Mac? 

The reason why I ask is because whenever I open iPhoto, there's a noticeable delay before I see any new Photo Stream photos appear, which suggests that those photos are being downloaded right then.

If this is indeed the case, given that Photo Stream only stores the last 30 days' worth of photos, does that mean that I'll start losing photos if I go longer than 30 days without opening iPhoto?
iPhoto doesn't have to be open. There's a background process running called iCloud Photos in Mavericks that runs as a system daemon that's taking care of bringing down your Photostream photos.

The photos are downloaded to ~/Library/Application Support/iLifeAssetManagement/assets/sub on your Mac. You can press Cmd-Shift-G in Finder and enter that path to browse the location. You'll see a lot of funny named sub-directories and in them: your Photostream photos. I don't recommend messing with this structure though.

What doesn't happen without iPhoto running is your photos getting imported in to iPhoto and organized in to events. So when you open iPhoto it's discovering new Photostream photos that have downloaded since the last time it ran and then importing those photos to bring them in to your iPhoto library. This is where the delay is coming from.

If you just want to view your Photostream without having to endure iPhoto you can try MyPhotostream which gives you a simple, read-only way to see your Photostream photos without having to launch iPhoto. It doesn't make iPhoto any faster on start, but if you need to get at your Photostream photos often it can make the process a little less cumbersome.