What you are saying is very similar to the statement that:
Absence of evidence is not evidence of absence
Suppose you have an autosomic gene A, which has a mutant allele a, causing an illness (or any other phenotype, for that matters). The particular nature of a makes its associated phenotype recessive.
You have three possibilities:
AA -> no illness
Aa (or aA) -> carrier, with no illness
aa -> ill
Now, let's take an aa individual (ill) and cross it with a sane AA individual:
aa x AA
All of the individuals of the first generation (F1) will be carriers (Aa) because the father will always give a and the mother always A.
Now if we breed them together
aA x aA
both parents have 1/2 probability of giving a and 1/2 of giving A. We will then have a proportion of:
1/2 Aa (1/4 A from mother and a from father, 1/4 vice-versa)
But this is just down to statistics. You have only 1/4 chances of seeing the trait reappearing, so you are much less likely to see it if they have 1 offspring then if they have 20.
Moreover, you have Aa offsprings in the progeny... this means that these could pass the mutant allele to the third or fourth generation.
Another important thing is that all we said is true if the first cross is
aa * AA
If it was
aa * aa
aa * Aa
The trait will (surely in the first case, and with 1/2 chance in the second) appear directly in the first generation.