In my design i am using LP2986 regulator, with 3.3V output and drop out voltage is specified to be .2V @ 200mA load. But when i put a load of 83mA dropout is increased.i.e if at this load input to regulator is 3.6V but output is not 3.3V it is 2.8V
This type of LDO needs a well tailored output capacitor ESR, if not in range this can cause instability. The ESR must be between 0.3 and 10Ohm's and the minimum capacitance 4.7u
I guess the problem comes from your input voltage.
In the datasheet, VIN specifies VO(nom) + 1V and you use 3.6V input to get 3.3V output, I think you are already out of the specification range.
Try increasing your input voltage, and the dropout should be improved