For the most part I agree with Bridgette. He could be busy, especially with his father in the hospital. He may be waiting for you to make a move, etc.
I am a little worried if you can see that he's on the site. Maybe he is dating other people he is meeting as well? Maybe he is unsure of his feelings for you as well.
Definitely give him a call/email. Mention going out again and you'll know for sure. If he blows it off and doesn't sound interested then you'll know for sure. If you two make plans then you will know that he was just busy. I agree with Bridgette though, don't let it become a pattern!
Him initiating contact after the date is a positive sign. Usually, if a man was not interested, he would not call to say that he enjoyed himself and call again at a later time. I'm sure that because he was on the dating site briefly that he was checking his messages - perhaps he is hoping to see one from you. He might need the reassurance that you are interested in him. Send him an email telling him how much you enjoyed your time together and you look forward to seeing him again and then ask him if he would like to go out sometime. With his dad being in the hospital, he might not be readily available so you might need to work around that.
"I neglected to add that he did call once last week, but didn't leave a message. I just happened to find it on my caller id. Had a one line email response from him a few days ago." He called you right after the date and told you what a great time he had and has made contact twice since then.. he is probably thinking the same way you are. If you really like this man, take some initiative and call him back. It really seems to me that this is what he is waiting for.
If you want to ask him out again, here's an example of what you could say: "You seem like a really amazing man, and I'd like to get to know you better. I'd love to go out with you again sometime. But if you're not interested, that's all right, too. I just didn't want to let this opportunity pass."
:::I hope this helps:::
Your more than welcome. :o)
Replaying how the date went and over analyzing things is normal. You really like him and are hoping for the same feelings in return - there is nothing wrong with that. I think you would both benefit if you initiated contact. I really feel that he has not lost interest in you, he is just not wanting to seem pushy and is probably waiting for a response on your part. If you don't feel comfortable calling him because he did not give you his number, email him or send him a message through the dating site you met on and reopen the lines of communication. You might even send him a "thinking of you" e-card and wish his father a safe recovery.