The voltage divider is not necessarily out of the question.
You can use a comparator with integrated reference, such as Maxim's MAX918, that has a total quiescent current of only 1.3µA and can operate down to 1.8V.
**broken link removed**
The reference voltage on this part is 1.245V, so you will need a voltage divider. However, since the input current is a maximum of 2nA, you can choose large resistors for the divider, avoiding current drain.
For example, you can choose the resistor to ground equal to 1MΩ, so the upper one would be about 820kΩ, resulting in a threshold of 2.25V.
The Thevenin equivalent of the divider is then 444kΩ. With that, the error due to the input bias current would be 444kΩ*2nA=0.9mV at the comparator input, which means only about 2mV at the divider input. Instead of a theoretical threshold of 2.25V, you would actually get 2.252V. Not bad!
You will get more errors due to resistor and reference tolerances than due to input bias current.
The total drain on the battery would be: 3V/1.82MΩ+1.2µA=2.85µA. That is pretty good.
The PIC will draw probably more current than that. One way to deal with that is to put the PIC to sleep and have it wake up on a port pin change, send out the code and go back to sleep. That way you minimize the battery drain when the RC is not in use.
Whenever it wakes up, the PIC can do a test on the comparator output and see if the battery is too low. If so, it would not light up the visible LED, indicating the battery is too low. Perhaps it should not send out any codes, seeing that the battery voltage could drop even more, due to the increased consumption, possibly resulting in faulty operation.