To be more precise, last info I read modeled the virus with exponential decay, with half-life measured in minutes to hours. After an hour (or 3h or 0.5h), half of the virus is already inactive¹.

Even after ~6 half-lives, remaining 1% of viral load is still potentially dangerous, but it's not a good basis for a test if you want it to be sensitive.

¹ Inactive does not mean destroyed. It may be possible or even easier to detect a partially decomposed virus, even with the current tests. Or not.