The first link to Amazon states in its specifications that the string at full length runs at 40W. And before your edit, you believed it was driven by a 30W LED power supply. The 30W supply would have explained this behavior at the full 5 meter length, but not when cut down to 1.5 meters.
Now that your edit states that it is only a 10W supply (can you explain? the link still shows a picture of a supply with 30W labeled on it), that would explain the behavior at 1.5 meters as well. Between the specs online and your 9.5W/m number, that would still put the power need somewhere between 12-15W.
@vitcatcu put the correct name to this effect - hiccup mode due to overcurrent protection.
When something doesn't work in a circuit, it is time to do some checks.
By what you say, you have tested the LED to be working when it is outside of the circuit, which means that then next thing to check is if there is any voltage driving the LED.
With the LED in the circuit measure the voltage at its pins. If the voltage is 0V, then it has to be something with the wiring (or maybe it is not meant to be always on).
A bad connection is quite often the culprit to many headaches.
Best Answer
Yes. The plastic outer globes are not sealed.