Hi Ralf,.
the case is in animals inasmuch as different, than that is doing about generative propagation and the diversity/variation of individual genes this is always low and this inbreeding depression after several generations arises (or can occur).
Alex,
so an Inzuchtdeperssion does not occur for vegetaiver propagation, the population is yes a clone and the genes be combined as in the generative propagation new, but remain identical.
Vegetatively propagated crops such as potato or Apple varieties can be (theoretically) indefinitely.
Practically it can cause but mutations in Meristemen (shoot tip), so that even in vegetatively propagated plants rung / spin-off / Cormel etc, that deviate from the mother plant. An example would be the type of Apple Red Gravensteiner is caused by random mutation from the (green) Gravensteiner.
Another reason for the deviations can be the mutation by single cells, sectors or layers in a shoot tip, which then leads to chimeras; Example would be konjac 'Shattered Glass', which should be developed from a pure green konjac.
What you are describing could be rather due to the accumulation of disease, so that the subsequent population are becoming less and less vigorous.
This is a problem that are also clones; z B potato varieties There are mainly virus that then cause growth depression in passage of time.
The variety 'Hansa' could eg be obtained by by Sproßspiztenkultur in combination with heat therapy back virus-free shoot tips were generated which then again virus-free "seed tubers ' were produced, which then again the original vigor" and the corresponding yield.
Hope this helps,
Bernhard.