LC, I hope you are saying that Villa Naxia already had responded saying there was space for your dates -- and all you have to do is confirm! Lucky you.
However, if you had e-mailed once with no response, don't wait until y ou hear from Villa Naxia before you try others on the list. Here's why: Most island hotels are family-run, not a big staff. The desk person has to take care of check-in & check-out and guest services, dealing with maintenance, BESIDES responding to phone queries, updating vacancy lists from online agency reports, AND (last of all) e-mails. The desk person will of course open up e-mails and -- if they have vacant rooms they want to rent, at your requested dates, he/she will quickly hit "reply." But, if the place is fully booked for your dates, answering your query with "sorry full" is lower priority. If a hotel is listed with an online agency, availability is shown instantly, but if a place has to handle all inquiries in-house, procrastination can happen.
For best results, booking late (1-2 months before trip), I advise 2-part strategy:
(1) -- immediately look at the others on the list.... and if there's one you like, book it! Not at the lowest non-refundable rate shown on agency websites, but at the slightly higher rate which says, no advance payment, free cancellation until (date about 2-3 weeks before your stay). Thus it is NO-RISK to book a back-up, if Villa Naxia is still #1 choice.
(2) Europeans know what to do if they want a quick answer: they phone. Why? Because a busy desk person can ignore an e-mail, but not a ringing phone! if no word from Villa Naxia, pick up your phone and CALL. Make your call between 9 - 11 GREEK time... because it's check-out time, and someone with fluent English will be at the desk for sure.