I am not able to download the attachment. Perhaps a forum issue. However, it is possible the silver coating is not 100% reflective. In this case, many bounces would result in significant loss. To investigate, you could set the source to deliver one ray and save a trace to a ray database. Then view it with the ray database viewer. You could also use Path Analysis if your version supports it.

You have multiple reasons for not all the light exiting the light-pipe

• As David wrote, silver is not 100% reflective. If you remove the coating and use “object default”, thus TIR, you will get around 25 lm instead of 22 lm. This tells you which amount of light (~3 lm) is loss to absorption by silver.
• Fresnel reflection from the entrance and exit faces of the light-guide will also count. If you change your first detector “Front Only” from 1 to 0, you can evaluate this amount of light. You get around 32.5 to 33lm (silver vs TIR): the 29lm incident from the LED and the rest is the reflected light: 3.5 to 4lm.

So your lightguide loses 3.5lm to Fresnel reflection and 3.5lm to Silver absorption, of which ~0.5lm is loss on the way back after Fresnel reflection at the exit.