FWIW, a workaround for the time being seems to be to translate the coordinates away from the y-axis before finding the convex hull:

schatzOloid[\[Delta]_Integer, \[Phi]_?NumericQ, \[Omega]_?NumericQ] :=
  Block[{px = 
     Table[{0, Cos[o], Sin[o]}, {o, 0, 
       2 \[Pi] - \[Pi]/Mod[\[Delta], 100, 1], 
       N[\[Pi]/Mod[\[Delta], 100, 1]]}],
    m1 = {{Cos[\[Phi]], 0, -Sin[\[Phi]]}, {0, 1, 0}, {Sin[\[Phi]], 0, 
       Cos[\[Phi]]}},
    m2 = {{1, 0, 0}, {0, Cos[\[Omega]], -Sin[\[Omega]]}, {0, 
       Sin[\[Omega]], Cos[\[Omega]]}}, x},
   x = Join[Plus[#, {0, 0, 1}] & /@ (Dot[m1, #] & /@ px), 
     Dot[m2, #] & /@ (Permute[#, {2, 1, 3}] & /@ px)
     ];
   res = TransformedRegion[ConvexHullMesh[{#1 + .1, ##2} & @@@ x], TranslationTransform[{-.1, 0, 0}]];
   BoundaryMeshRegion[res, PlotTheme -> "SmoothShading", Boxed -> True, 
    Axes -> True, AxesLabel -> {"X", "Y", "Z"}, Ticks -> None]
] /; \[Delta] > 2

schatzOloid[37, 0, 0]

I ran the following from the notebook.

Remove[schatzOloid0]
schatzOloid0[\[Delta]_Integer, \[Omega]_?NumericQ] := 
 Block[{px = 
     Table[{0, Cos[o], 1 + Sin[o]}, {o, 0, 
       2 \[Pi] - \[Pi]/Mod[\[Delta], 100, 1], 
       N[\[Pi]/Mod[\[Delta], 100, 1]]}],
    py = Table[{Cos[o], 0, Sin[o]}, {o, 0, 
       2 \[Pi] - \[Pi]/Mod[\[Delta], 100, 1], \[Pi]/
        Mod[\[Delta], 100, 1]}], 
    m = {{1, 0, 0}, {0, Cos[\[Omega]], -Sin[\[Omega]]}, {0, 
       Sin[\[Omega]], Cos[\[Omega]]}}, x},
   x = Join[px, Dot[m, #] & /@ py];
   ConvexHullMesh[x,
    PlotTheme -> "SmoothShading", Boxed -> True, Axes -> True, 
    AxesLabel -> {"X", "Y", "Z"}, Ticks -> None
    ]
   ] /; \[Delta] > 2

Animate[schatzOloid0[37, \[Omega]], {\[Omega], 0, \[Pi]}, 
 AnimationRunning -> False]

I then hit the play button and let it go for a couple of minutes. This is in version 11.2, running under Linux. I did not notice it stop and did not get an error message window. During this time I twice reevaluated the definition cell and also stopped/restarted the animation. Assuming I ran this as you expected, I do not know if it is platform dependent issue or if something else weird is going on (this remark is only with reference to the Animate issue, not the other one noted regarding parameters that are zero).

schatzOloid is not an image of code, but anyway: find please in the appendix the notebook and the system Information about the machine to your comfort; Run the Animate commands each at least for a minute - just click the arrows and observe - with schatzOloid0 (2 Parameters, former schatzOloid) as well as with schatzOloid ( now 3 Parameters) - both loose seemingly the definition (in the original post the penultimate picture) and showing by chance the message about the beep, which is not in the notebook, but in the original post (last picture), because that's to my knowledge the only way to present it.

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