I can't specifically say about house finches, but most songbirds only use the nest once. That being said, I had a phoebe that nested on the same spot on the front porch lamp for five years. I never cleared the nest.

Some birds build nests & wait to lay eggs, so I'd be prone to keep it up for a bit longer. Always be on the conservative side before removing an unused nest. Birds don't typically reuse nests once eggs hatch & babies fledge. That's when you would definitely want to clear out the nest. In this case, it's hard to say.

Nicole

I had some Robins last year build a nest on the end column of my front porch last year. My pest control co. asked if I wanted them to take it down. I told them no, not until we knew for sure they were done using it. After about two weeks, not sure if it was the same family of Robins, laid another round of eggs, and started the process again. After those birds were finished, the pest control co. took the nest down around July. This year, another family of Robins built another nest in the same place. I left it there but they only used it once. It will be taken down in July again.

Well, we ended up taking it down after about a week since the birds didn't come back and it was a little sad to see the empty nest every time we came down the stairs (we could see it from inside the house). But then this week a pair of house finches built a new nest on a different column on the porch. I hope they have better luck! We've had two nest failures at our house this season and we have to keep telling our four year old daughter that the birdies are gone, they must have grown up and flown away...