Hail,
I don't believe there is a low voltage cutoff for rcr123 battery but I could be wrong. When your battery protection circuit cuts in, the light turns off and you click it off. Without load, the battery voltage will recover and when you click it a little later the light turns on. Depending on how low the battery is and how much voltage has recovered, the subsequent on time will differ. However, given the battery will get lower and lower, you on time will become less and less until maybe it only blinks. At the same time, the time it takes for the light to be able to light up is lengthen as it needs more time for the voltage to recover.
There are a few ways you can find out definitively.
1. Using a linear power supply, set it at like 2A CC and 4V. Tap it to the light and set light at max. Slowly adjust the voltage down and see when the light will cut out. Then set at 3.1V and do the same. Then set at 1.5V and do the same.
2. Find an unprotected 3.7V rechargeable battery. Remove the head of the light and using wires/clips, etc and a battery carrier, tap the battery directly onto the light. Set the brightness to higher than medium and put a DMM on the battery. Watch the voltage drops. If it drops too fast, lower the brightness. Let the voltage continue to drop and see if the light will turn off. If the light does not turn off as the voltage drops below 2.7V, you can manually disconnect the battery to protect it or you can let it drain to the point you are convinced that the light does not have a low voltage cutoff. Below 2.5V, you are likely to damage the battery. I onced dropped the voltage on a unprotected lithium to 0V and took me quite a while to revive it but that was just luck.
3. CAUTION: doing this may (and likely will) ruin your battery so only do this test if you are willing and can afford to have one of your batteries kiss you goodbye. Put an unprotect rcr123 or cr123 in the light, turn it on to like at least med. Leave the light on until it turns off by itself, then leave the light alone for at least a few more days at that on setting. After a few days, take the battery out and measure the voltage. If your battery voltage is below 1V, then no low voltage cutoff in the light.