Although having a wide genetic base is preferable for the long term, most named OP varieties already have a relatively narrow gene pool, due to selection. That narrow genetic variation is almost the definition of what we think of as a "variety", and what makes it unique.
Out-crossing plants can suffer from inbreeding depression over time. I've witnessed this in a squash that I've saved for several generations. For out-crossing plants (especially corn & brassicas) seed should be saved from as many plants as possible, sometimes to the point where a large population is required. I may need to bring in new squash seed to refresh my favorite variety, and hand-pollinate with a pollen mixture from all plants.
Plants that are predominantly self pollinating (such as beans, tomatoes, and peppers) rarely suffer from inbreeding depression. I have a couple beans that began as a single survivor, and are still exceptionally vigorous after several generations. Likewise, I have observed no reduction in either yield or vitality, for peppers which I have grown in isolation for several successive generations. I haven't noticed a difference in tomatoes either, except for one variety which seems to be slightly less productive... and that may be more a result of soil depletion (my main plot was fallow this year, so I will be interested to see if yields improve).
An interesting point about seed saving philosophies. The conventional wisdom is that when you save your own seeds, the variety will adapt to your soil & conditions over time. I believe this to be true - to some extent, and not just because of genetics. Although I am not a geneticist (
@seedcorn could probably explain better than me) I believe that two factors are involved in such improvements: genetic selection, and genetic expression. For there to be
selection, there has to be variability in the genome to select
from. As I've mentioned, most named varieties of self-pollinating plants are homozygous (genetically identical); so they are basically clones, with their offspring being identical to the parents. Genetic
expression, on the other hand, could involve the activation of dormant genes already present, even in homozygous populations. IMO that genetic expression of dormant genes - and the improved vigor which can result from using fresh seed - are the most likely reasons that some varieties improve when seed is saved.
I wish I could give you a better answer specifically regarding inbreeding depression in tomatoes,
@digitS' . I find that my struggle with successive generations of tomatoes is trying to
preserve homozygosity... I keep finding the crosses that some tomato growers claim don't happen.
