It would be way too much of a generalization to say that all individuals on the spectrum can't keep secrets. I came across a message board titled wrongplanet.net when researching the topic and there are people with ASD who can keep a secret just fine.
Of course, individuals on the spectrum tend to have a hard time with social norms and understanding the "rules" associated with keeping secrets is no different. Typically, they won't understand the social situations that surround keeping secrets. Whether its the autism or the combination of that and his young age, one thing is for sure, Curt can't keep a secret to save his life.
A few days ago, Curtis broke a small figurine of his mothers. It was an accident and he felt bad about it. Mom was exercising and I told him I was sure I could fix the two broken areas with super glue. The repair on the porcelain went fine, much smoother than Curt's ability to deal with his accident. He asked if I could keep it a secret and keep it between us. I told him he wouldn't get in trouble if he told his mom and that we had fixed it, but I was also curious if he could keep it a secret, since I'd never actually seen him keep one successfully before.
As the glued figure sat drying, Laura sat next to him with no knowledge of what he had done. As she asked a couple of unassociated questions, he broke down and hugged her, burying his head in her chest for a long time. SHe was obviously curious about his condition. He didn't spill his secret, but didn't exactly play it cool either. I told her what was going on and after a little time, Curt was relieved of the burden of his secret. It's typically excruciating for Curtis to try to carry any secret at all. This blog post from Autism Speaks does a good job of pointing out some of the difficulties I see in Curt when he attempts to keep a secret.

"Those with autism spectrum are concrete thinkers and exceptionally honest – if asked a question, they will respond with the truth, without taking the time to analyze and reflect what should be said and not said. Thus, secrets are hard for them to keep for any length of time."

This is certainly true for Curtis. Not that the broken figurine was a secret he had to keep. However, even though it was his idea to keep the secret, he simply couldn't handle it. As soon as his mom asked him something, he folded.

"those with ASD will usually tell it like it is – revealing to parents, siblings, their friends, acquaintances and perfect strangers things that shouldn’t be told. This can be either a positive or a negative; how others handle the completely honest statements made by the child with ASD will determine how much trouble will follow. If a very young child, most adults will laugh over the blunder; if an older adolescent or adult, grave consequences can result."

As many of Curt's qualities go, the lack of an ability to keep secrets is more endearing than anything else. He'll usually tell you what is in a wrapped present or reveal anything meant for a surprise.

"For the child with autism spectrum, this whole business of keeping secrets can be very confusing. Appropriate instruction on secret keeping is both difficult and delicate and should be tackled carefully by parents and teachers. Even after intensive instruction however, making this type of judgment requires split-second analysis of multiple factors, both concrete and humanistic. So don’t be surprised when the kid spills the beans."

Greg, Dad