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The paper studies violation of conventional rules of SUSY quantum mechanicsfor the centrifugal potential V(r) within the limit-circle (LC) range. Aspecial attention is given to transformation properties of the Titchmarsh-Weylm-function under Darboux deformations of the reflective Kratzer oscillator:centrifugal Kepler-Coulomb (KC) potential plus a Taylor series in r. Since ouranalysis is based on Fulton's representation of a regular-at-infinity solution[Math. Nachr. 281, 1418 (2008)] as a superposition of two Frobenius solutionsat the origin, we refer to the appropriate expressions as theTitchmarsh-Weyl-Fulton (TWF) functions. Explicit transformation relations arederived for partner TWF functions associated with SUSY pairs of centrifugalpotentials. It is shown that these relations have a completely different formfor Darboux transformations (DTs) keeping the potential within the LC range.  As an illustration, we use regular nodeless Frobenius solutions to constructSUSY partners of the radial r- and c-Gauss-reference (GRef) potentials solvablevia hypergeometric and confluent hypergeometric functions, respectively. Weexplicitly demonstrate existence of non-isospectral partners of both radialpotentials in the LC region and obtain their discrete energy spectra using thederived closed-form expressions for the TWF functions. The generaltransformation relations for the TWF function have been verified takingadvantage of form-invariance of the radial GRef potentials under double-stepDTs with the so-called 'basic' seed solutions (SSs). Similarly we directlyratify that TWF functions for three shape-invariant reflective potentials onthe half-line -- hyperbolic Poschl-Teller (h-PT), Eckart/Manning-Rosen (E/MR),and centrifugal KC potentials - do retain their form under basic DTs.

Breakup of SUSY Quantum Mechanics in the Limit-Circle Region of the Reflective Kratzer Oscillator