lower current than expected through simple circuit powering laser diode
Did you check the power supply from which you power the LASER branch? Summing all the voltage drops in that branch gives 
0.02V + 4V + 12mA &times; 49&Omega; = 4.6V, which are not the 5V you should have.

It seems that your power supply cannot handle so much current and is dropping out.

Check that your power source for that branch is not overloaded by other loads in your circuit, since 12mA seems a bit too low to overload a power supply, even small on-board regulators. 

EDIT

After you corrected your question and added the LASER's datasheet it becomes apparent that you are outside of that LASER's specs. Just for a tiny 0.1V, now, but you could have damaged your laser during power-up when the whole 5V could have been fed to the LASER module. 

That module expects 4V constant voltage supply (&pm;0.5V max). Connect the module to a bench power supply set at exactly 4V and try if it's still working. If it is, then follow the advice in a comment of @sstobbe: get rid of R2 and put a diode in series with the module. 

For extra safety, since at low currents diodes have a smaller voltage drop and so a 0.7V drop cannot be guaranteed (e.g., it could be 0.56V, depending on the diode actual model), it would be better to put two diodes in series, at least initially, just to be sure you work on the lower side of the specs. 

After you measure the actual voltage drop across those diodes you might remove one and see if it works still in specs (but if it works with two diodes, maybe it's better to leave it that way, just in case your power rail has a small hiccup).