I would do a follow up e-mail. It is always good to be in communication with your prospects and current clients. But don't be overbearing or come off needy. Something along the lines of,
Just wanted to catch up with you on your search to fulfill your vacancy. I hope the search is going well and the right candidate comes along.
I also look forward to being able to assist your company with our ongoing site maintenance service.
If you have any questions or concerns, feel free to reach out to me by e-mail or phone.
Once you stop communicating, you are going under the falsehood that companies will always remember to return your email or phone calls. Keep in mind, they are just as busy as you are on a typical day. Things get missed/forgotten, and your reminder's and the fact that you are identifying with them from prior conversations are CRITICAL to developing a lasting relationship.