A possible new client messaged me about an upcoming stay. I replied but haven't heard back. How long should I wait until I message them again and ask if they're interested?
You can send another message after 24 hours. If you don't hear back from them, then they are probably meeting with other potential sitters and it really depends if they find someone else they like from among those. Perhaps they'll get to you. Perhaps they won't.
Just give them 24 hours and then archive the request. People don't like to be hounded and, unfortunately, this is the way Rover advises its customers to go: contact several, interview and select from among those. You never know what is going on and I wouldn't worry about it.
Personally, once I respond I leave it at that. I wait until they reach back out. If it's been a few days (2-3) and no response, I might send a message if they found someone but it depends, for me, how much we spoke. If they owner had a conversation with me describing their pet and what they need and mentioning the want to have a meet and greet, I'll do the follow up. But other than that, I'd just let it sit for a few days and archive it for no response.