wiring for illuminated 3 way toggle switches
Assuming your switches are similar to the Leviton 1463 (wiring diagram taken from their site):

Leviton 1463 wiring diagram http://www.leviton.com/OA_HTML/ibcGetAttachment.jsp?cItemId=wWm55e.lPvCEg-uYaozWiw&amp;label=IBE&amp;appName=IBE&amp;minisite=10251

there is a resistive bridge between the two travellers that is tapped to feed one end of the pilot light, with the other end connected to the common terminal.  When you put two of these in circuit and put the switches in opposite positions, the net effect is that of a resistor-bridge with the pilot lights shunting two opposite legs (which two depends on the switch positions).  When all the parts work, this means that both pilot lights are effectively in parallel, and will both be on with the switches off.  However, if one of the legs that isn't shunted by the pilot lights at the time is toast, the other pilot light will not light.

Either that, or one of the pilot lights itself is gone.  Either way, you'll be replacing a switch.  As to which one? Well, you can test them with a multimeter:


Turn off the circuit.
Remove one of the suspect switches.
Put your multimeter on the Ohms setting (a 200kOhm or 2MOhm range is a good starting point if you have a manual ranging meter)
Measure from the common to each traveler terminal -- one should show a dead short, the other should show a high but finite resistance (somewhere between 40-50kOhm and perhaps 500kOhm or so).  If you get an infinite (open circuit) reading on the meter, then you've found the dud.
Flip the switch and repeat the test.  Again, an infinite reading means the switch has gone bad internally and needs replacing.
Reinstall the switch under test if it passes, and repeat this procedure with the other switch.