Neville is neither dead, nor in immediate danger. In light of what happened to Hermione, in particular how all their precautions were bypassed, they will want to up Neville’s security level, and I think it likely that this will come up before the arc is over, but I would not say that it has immediate level urgency.
So, uh, why isn’t Harry trying to save Neville?
I have experiments to run
There is research to be done
On the people who are still alive
Neville is neither dead, nor in immediate danger. In light of what happened to Hermione, in particular how all their precautions were bypassed, they will want to up Neville’s security level, and I think it likely that this will come up before the arc is over, but I would not say that it has immediate level urgency.