A PM goes to your outbox when you hit submit. When the person opens the PM, it gets transferred to your sentbox. You can view your outbox to see if the message is still there. If it is, the person has not opened it yet.
Sometimes I don't open my PMs right away. I get them sent to my e-mail, and usually I'll see them there first. I don't open it here on the site right away because I've already seen it in my email. Maybe that's what is happening in your case. The person has to open the PM here on this site for it to get transferred to your sentbox. Maybe they are reading it in their email and then not opening it here right away.