With one resistor, if one of the LEDs fails, then the wrong voltage will be going through all of the remaining LEDs, causing them to fail prematurely. Before the failure, it was (voltage-resistance)/4. After the failure, it becomes (voltage-resistance)/3. Too much voltage through the three remaining LEDs.

With multiple resistors, the failure of one LED does not change the amount of voltage going to the other LEDs.
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Tony Fabris