There are several things here...
The NiMH cells you chose could, in theory, support 2 mA current draw for 30+ days based only on the mAH rating. However, there is self-discharge to consider. This Wikipedia article says that a typical NiMH battery will loose 5-10% of it's charge the first day and about another 1% every day after that. My experience is that it is true for new batteries only, and older batteries will self-discharge much quicker. My cordless drill, for example, would be useless 6 weeks after a full charge when new but now is useless after only a week-- when not being used at all during that time.
Lithium rechargeable batteries, however, have a much lower self-discharge rate. Which is why I'll be buying a lithium based cordless drill real soon now!
As for your question... The problem with using a diode is that the voltage drop is not always 0.6v. At low currents it could be much less. The datasheet for the diode will contain a graph showing the voltage drop vs. current. You say 2 mA, but it will more likely be less than 0.5 mA most of the time with pulses greater than 4 mA (just a guess). So when it is taking 0.5 mA the voltage to the module might be too high.
The ideal device is a Low Dropout Linear Regulator (LDO) that is designed specifically with this in mind. Sorry, but I don't have time to find one right now. But there are LDO's designed for running off of a battery. When the battery is new it regulates like normal, but as Vin drops below the ideal Vout the regulator will stop regulating and Vout will basically equal Vin. Not every LDO will do this! If it doesn't say in the datasheet then you must assume that it won't do this.
Another idea would be to create your own "lame switching buck converter". The business end of the converter is a simple MOSFET feeding Vbat to a storage cap. The output of the cap feeds your module. If the cap voltage drops below, say, 2.5v then the MOSFET turns on. When the cap voltage reaches 3.3v the cap turns off. A simple voltage comparator with hysteresis can do this. Look for a super low power comparator, since you don't want this thing to consume more power than your module. Make the cap large enough that the turn on/off rate of the MOSFET isn't too fast. Below 10 KHz, or maybe even below 1 KHz. An inductor in series with the MOSFET might not be a bad idea, to reduce the peak current from the battery. I would rather use an LDO than this, however, as it would be much easier to get right the first time.