Hi Priscilla, you're probably not doing anything wrong. There is a bug we've found in the 'reply to a contact request' message that means they don't always get delivered. It's being fixed as we speak and will be going into the next code fix (apologies if that's what's caused you trouble).
Have you tried sending a personal message? That will generate an email to your contact, so they'll be notified in both their network inbox, and their email inbox. Just go to your contact's profile page, and you'll see a 'send a message' link under the picture on the left side of the page. You can also send a message from inside your inbox if that's easier.
FYI, we're expanding the email notifications function (which will be deployed at the end of July), so that you receive more notifications when people respond to your posts or comments. That should help everyone keep track of conversations and responses in the network a bit more easily.
Hope that all helps -- let me know if it doesn't work.
Di