Hi Pete,
Welcome to the forum. Yes, in principle it's possible, but depends on exactly how low a power consumption you require and whether it's an "off the shelf" remote control or a "custom" design.
The two basic methods are to sleep/nap the PICaxe for short periods (testing for IR each time it wakes up) and/or running the PICaxe at a slow clock speed (e.g. setfreq 32kHz) until some IR is detected. A third method of using an interrupt is not normally appropriate/possible with a PICaxe, particularly the non-X2s.
You need to measure/decide how long a burst of IR is available to "wake" the PICaxe and then it's possible to decide on the nap and/or clock speed parameters, and the general structure of the code. Note that some commercial Remote Controls automatically repeat their "message" several times (however long the button is pressed), others may continue repeating until the button is released.
Cheers, Alan.
PS: I've just noticed that you quote 08M rather than 08M2. Are you referring to the project board or to the actual PICaxe chip that you plan to use? I believe the 08M chip may have more restricted frequency capabilities.