It's called Snapchat for a reason

Members of anonymous online message boards claim to have accessed hundreds of thousands of private photographs shared on Snapchat, a popular photo sharing service, just weeks after a celebrity hacking scandal drew increased attention to online privacy concerns.

But the photos do not appear to have come directly from Snapchat.

Instead, the collection of photos of noncelebrities, which some claim is as big as 200,000, appear to have come from the accounts of people using Snapsaved, a smartphone tool that its creators said would allow users to store photos from their Snapchat accounts that normally disappear after 10 seconds.

Links to Photos Said to Be Stolen From Snapchat Users Flood Message Boards - NYTimes.com

The story behind Snapsaved is interestingly mysterious and well worth reading, but to the point: there's an app well suited for keeping photos and video longer than 10 seconds and it's called f**king Messages.

No charge for that pro tip BTW.