Unconfirmed stays months away?

Archive it immediately. Archiving doesn't affect your ability to accept or communicate with those owners in the future.

If you do receive inquiries or offers for that same time period, then you would meet with the new customer and decide which one you wanted to pursue. At that point, you would contact the first customer, ask about the status and let them know that you have received another offer for that period and they will need to decide about you within 24 hours. You really can't hold open dates when you know the client is meeting with others and that it could take forever for them to make a decision.

Do what is best for you.

In cases where the date is more than 2-3 months out, I archive the request. I tell the client I will pencil them in on my personal calendar and I will contact them if someone else asks about the same dates. If someone does ask, I tell them I have someone tentatively booked for those dates and that I will be back in touch with them within 24 hours. I contact client #1 and ask if they still want me to board/house sit and that another person has asked for the same dates. Client #1 can either pay or potentially lose the booking. I then communicate with #2 the results of my discussion with #1. I believe in the principle of first come first served, and client #1 gets first priority. But I only give them 24 hours to decide and pay, otherwise I move on to client #2.

Archive as "owner didn't reply". I have a repeat customer who now calls me and wants to find out if certain dates are available for them to book. I check my private calendar and say yes. They are "professionals" but say they don't know how to use the rover system so they "...will call rover...." I tell them their dates aren't reserved until they book. Of course they don't. I don't even bother putting them on my private calendar any more. Since your potential customers are interviewing other sitters, if I were you, I would archive and move on. That is one of many learning cures we all go through.