  Let K be an algebraically closed field. For a finitely generated graded K
algebra R, let cmdef R := dim R - depth R denote the Cohen-Macaulay-defect of
R. Let G be a linear algebraic group over K that is reductive but not linearly
reductive. We show that there exists a faithful rational representation V of G
(which we will give explicitly) such that cmdef K[\sum_i=1^k V]^G >= k-2 for
all k. We give refinements in the case G = SL2.
