First off, I would practice more as I believe it is 100% when practiced, I've only had it drop off once and that was due to my error rather than the technique itself not being 100%.(nor have I ever had any indication from anyone that it gave away the "secret" anymore than when you pull the ends off, but lets face it the audience thinks the ends stick together anyway even when they are examined).
I think there are two very different situations regarding dropping the little piece.
1: If you drop it and still have a hold of the two ends, then I would do the "loop" move to show it is a solid ring, and then throw the "ends" back on, and transition right into the ends going on and off the rope quickly.
2: If you drop it and have already released the ends(this shouldnt ever happen with proper timing because if you miss the little piece you should still have the ends). In this case I think a quick joke, simply putting the little piece in your pocket and then proceed to do the ends fusing sequence once or twice and then retrieve the ends from your pocket saying you knew they would come in handy and then put them back on.
I think that overall, the trick is not some super mystery that will leave the audience wondering about the secret for months to come, and is more of visual fun magic which is "in the moment". To that end, I don't think it matters if they know the secret because all the fun and entertainment is in the routining and energy you put into it.... so don't sweat the small stuff.
However, this advice is assuming you are at 99% or 100% with the move... if you aren't, then keep practicing and leave it out of the routine until it is.
This problem really boils down to the difference between a performer and an amateur magician.... When a great performer has a trick go wrong or a secret get exposed or whatever else, it is moved over quickly and smoothly and the audience doesn't care because the magic is about the MAGICIAN, not the trick. Conversely someone who is uncomfortable in front of an audience uses the *trick* as the focal point, so if something goes wrong with it, then all attention is on the magician and they will bomb because they werent expecting it.
So basically, work on becoming comfortable with an audience and performing and you'll never need to worry about messing up a routine because you'll have the confidence they are there for YOU and not the tricks, so even if the tricks don't work everything will work out fine!