how can I redirect the grepped output of tail -f to a file?

I want to do this:

tail -f /var/log/apache2/access.log | grep 'POST \/review'

But I want the output to go to a file and I want this to run constantly for a day or two.

I tried a simple script with the above and redirecting output to a specific file, then running that with nohup, but it doesn't dump anything into the file or to nohup.out.

Is there maybe another way of doing this without tail?