This means when you try to use it again, there is a cold start penalty.
You can architect your app around this a little bit, like having your web service "wake up" your database when you suspect one of your users is about to use it.
I enjoyed using Neon in a small project but the cold start was a significant penalty to the point where you might just want to send keep-alive transactions all the time, but it seems like they've made significant improvements to that earlier this year[1].