Listening to old songs, he lamented that youth cannot be kept.
Tips
history
The phrase '青春留不住' recurs across Chinese pop lyrics and ci poetry; 朱敦儒 (Zhu Dunru, Southern Song) wrote '青春留不住,鬓上已堆霜' in 《鹧鸪天》. It is now a stock line in Mandopop (e.g. 张信哲, 张学友 covers).
grammar
留不住 = 'unable to keep / make stay.' 不住 is a resultative complement meaning 'cannot succeed in making something stay (put).'