The problem is that leChopShape will return a list of the new shapes - and you have no idea which is the one you want to do subsequent chops on. Now you're not removing the gaps you're chopping out (I suspect you want to though) - but even if you do that, it's not going to solve the problem - fundamentally you will end up with two or three shapes when you chop the remainder of the donut (depending on whether you keep the shapes in the chopped region). If you pick the wrong shape (you have arbitrarily chosen then cadr), then the next chop will return nil because there was nothing that was chopped.
So I think you need to do something like the below - use dbGetTrueOverlaps to find the polygon underneath the mid point of the next segment to be chopped (I compute the midRadius and then a point half way through that segment) - and then chop that. In this example I also remove the chopped region (you must tell it that the chop points are a closed polygon for that to work) - whether you want to do that or not is up to you (this is the t t arguments in leChopShape).
I also added local variables too, for good measure. Note that in the code, you might be able to use cc_mainR rather than computing cc_midRadius (I'll leave that to you - I only spotted this upon reviewing the code).
procedure( ConstructCog(cc_mainR cc_SourceNLength cc_NPolyOvelap cc_NWidth cc_PWidth)
let((MainCirc NumOfSegs SegWidth SegNWidth cc_InnerR cc_OuterR cvID donutID NSegAngle
PitchAngle cc_TempRadius cc_midRadius i_FirstX i_FirstY i_secondX i_secondY
identifyX identifyY NewShapes)
donutID=dbCreateDonut(cvID "Metal2" 0:0 cc_OuterR cc_InnerR)
;hiZoomAbsoluteScale(cvID 1) ; want to zoom to fit, doesn't work
for(i 1 NumOfSegs
donutID=car(dbGetTrueOverlaps(cvID list(identifyX:identifyY identifyX:identifyY) "Metal2" 0))
;dbCreateLine(cvID "PPLUS" list(0:0 i_FirstX:i_FirstY i_secondX:i_secondY 0:0))
;leChopShape( donutID list(0:0 i_FirstX:i_FirstY i_secondX:i_secondY 0:0) nil nil 300 )
NewShapes=leChopShape( donutID list(0:0 i_FirstX:i_FirstY i_secondX:i_secondY 0:0)
t t 300 )