It honestly depends on why they said no. Sometimes it is timing related (they’re too busy or maybe your event is too soon), sometimes they don’t have enough budget left, sometimes it’s a bad fit. I always like to ask explicitly - people won’t always tell you but when they do, it’s helpful!
Not having enough budget left is often the easiest to solve because the fix could be discounting your price or switching them to a lower sponsorship tier.
Bad timing is harder to fix, but gives you info to reach out earlier for your next event.
In terms of it being a bad fit, it’s important to find out why - maybe they don’t target students, maybe they don’t have internships at all, etc. There is a small chance the reason it’s a bad fit is due to not fully understanding your event/what the benefits of sponsoring are, in which case you can correct and turn it around.