If you can't view a photo from time to time, its probably because the server on which the photos are saved is going through maintenance or can't be accessed for one reason or another. So, if a photo you can see today is store on Photobucket, if you can't view it another day, its because there is a problem accessing the photo on the Photobucket server. None of the photos are stored with the Forum, they are just referenced by the Forum.
And yes, sometimes firewalls and privacy settings can interfere with viewing photos, but if you have viewed them once, you shouldn't have any problems later if you are on the same computer.