Why would my battery die as it runs?

Your battery would die if the car is using more power than the alternator is providing. It could be something using power - it could be the alternator is bad. Is the battery light on? That means you have a bad alternator.

Check your battery voltage. With the engine off, it should be around 12.5 volts.With the engine running, it should be around 14.5 volts after start up. It might drop down to 14 volts after 15-30 minutes of running.

oops 2000, then still batteries die after ten and need to be replaced~

137 ain't too much, but a rebuilt would be much less~

$35 from pickNpull~

deffo alternator in the uk its as easy as remove and exchange replacement ie: discount on the alternator if you give them yours which the will refurb also try some belt dressing (spray) to see if that works could be a slipping belt if you lucky :)