Maybe an example will help.
Commented example capx: StopGo.capx (r168)
When you press "GO" it sets your score to 0 and starts counting up (based on dt * 1000).
When you press "STOP" it stops adding to your score and compares that to your best score.
If your current score is less than your best score, it saves that as the best score in webstorage and updates the display.
The "Best Score" starts out at a high value, until a better score is made/saved.
If your game still isn't saving, you might need to share your capx (can use dropbox.com) so someone can test it and see what's going wrong.