all feeds are archived and kept for 45days which means you can download them in 30min segments.
if you hear something good, just note down the time and go to the link below a little later. it's easier being in the UK because Zulu time is GMT and the archives work on Zulu time.
go here:
http://www.liveatc.net/archive.php choose which ATC Region, date, and time you'd like to download then press submit.
then on the next page, just above the weather map click on 'listen'.
and well, there you go.