555 Timer Stops working after a few seconds
Yes you are certainly over driving the LED without a current limiting resistor.

Define the LED max Current and choose a series  R , Imax=Vdrop/R

How bright must this LED be to work well in 1ms? I suggest you need several watts.

e.g. 3 large SMD white LEDs in series capable of 350mA pulses for 9.x V then drive direct from 555 output is possible with 10 Ohms in series.



Simulation 

If you buy this 8.4V LED from Digikey, also get some  Resistors in the range of 2 to 10 Ohms 
then consider 555 Vout has 2.5V drop @ 200mA so 12V ecomes 9.5V  max compute (Vout - Vf(LED))/If= R  e.g. (9.5-8.4)  /220mA = 5 ohms,  400 mA  maybe 2 Ohms, never 0.  ( there are better designs)