  We analyze the fate of dynamical systems that consist of two kind of
processes. The first type is supposed to perform a certain function by
processing information at a required high accuracy, which is, however, limited
to less than 100 percent, while the second process serves to maintain the
required precision. Both processes are assumed to be subject to a trade-off
between cost and precision, where the cost have to be paid from renewable but
limited resources. In a discrete map we pursue the time evolution of errors and
determine the conditions under which the fate of the system is either a stable
performance at the desired accuracy, or a deterioration. Deterioration may be
realized either as an accumulation of errors or a decline of resources when
they are all absorbed for maintenance. We point to possible implications for
living organisms and their perspectives to avoid an accumulation of errors in
the course of time.
