All the way with 3 AAs. The 28X1 is at heart a PIC16F886, so has supply ratings 2-5.5V.
If a project board however calls for 4 x AAs, a series Si diode (or two) in the PICAXE supply line usually does the dropping trick. Si diodes drop ~0.7V when working of course, & this remains pretty constant over a wide current range.
Over the years I've seen diverse circuits even using series LEDs (reds drop ~1.8V, greens ~2.0V) for such regulating tasks. Although load current drain will be limited to the ~10-20mA LED capabilities,the glowing LED(s) can make a handy (& cheap) "what's going on" ammeter.
Diode droppers may seem pretty trivial when 3 terminal 7805s are so well established, BUT the whole 78xx family needs a supply a good 2V above their delivered output voltage. Hence if 5V is needed from a 6V supply, perhaps to run a PICAXE, a 7805 will not be suitable.