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Hello Mrs Montgo,
Sorry for not seeing your message earlier.
This is the first time I've heard anyone have this issue, but it does not surprise me at all. Those pegs are designed to print upright without using support material (I assume that is how you printed them). My guess is that they are breaking between the layers that the printer makes. The slot in the pegs is there to allow them to be squeezed slightly when a gear is pushed onto them. This can put stress on the layers.
A general 3D printing technique is to print with the layers going in a direction similar to the way you would orient wood grain, for strength, in a piece of furniture. I did not take my own advice here, for the sake of making it easier to print. So, I will suggest that you re-orient the pegs 90° for printing (with slot vertical to print plate). By laying them on their side the "grain" of the plastic layers will be going vertical, when stood up. Like a baseball bat. You will probably need to use the support material function, which will involve a bit more cleaning post printing.
I suggest "Simplify3d" for a printing app. Nice control for support.
I hope this helps. Please do reply back to let me know how it works.
-- Bernie (SSW)