Hi,
no, that should not happen. I tried it with a small molecule, and C4v, C2v, C1v, C1 gave all the very same energy. Did you try Cs also (the difference is just that the mirror plane is taken as xy instead of xz)?
Please read in the C4v symmetric coordinates again, run define and use susy instead of sy down to Cs. Save the coordinates and run an energy calculation. Call define again and force C1v symmetry with the Cs coordinates (they might be rotated to change the mirror plane).
Then the next ridft run should give the same energy. If not, please send this as a bug report to turbomole at cosmologic.de.
Regards,
Uwe