I would love to see Harry happily dating someone wonderful. However, if he is, he and his girlfriend must be wearing Harry Potter invisibility cloaks. Because it's just not the Press after photos, is it? Everyone has a cell phone and plenty have Instagram accounts and go on Twitter.
No matter how Harry could try to disguise himself it would only take one excited Harry fan on Twitter saying "I saw Prince Harry last night with his friends at --- and there was this blonde girl with him and...!" And his secret would be out.
When he was in the very first stages of dating Cressida Bonas just after he'd come back from Afghanistan, a fan posted a very blurry photo on the Internet of him dancing with her (she was then unknown) in some obscure Notting Hill club. There was instantly a lot of Internet chatter about who it could be, "It's not Chelsy, she's too short!" And this went on for days.
People refused to believe that he was dating CB until it was actually staring them in the face, but that's beside the point, which is that a high profile person like Harry just wouldn't be able to keep a steady girlfriend a secret.
There is just a tiny chance that he might be dating a young aristocrat whose father has vast estates they could hide in as well as going up to Sandringham etc. However, if they wanted to go out together in London, unless they go about in complete disguise somebody would be spotting them sooner or later.
So, I think, unfortunately Harry isn't dating anyone regularly at the moment, least of all Chelsy. I just feel that ship has well and truly sailed.