Do the effect of inbreeding depression disappear after the first generation of outbreeding?
This depends on if you are talking about animals in the wild, such as isolated populations, or humans, or whether you mean research animals. Inbreeding tends to breed homozygosity, so as you said, if you have a recessive disease causing allele within a bloodline, then even if only one of the founders was a heterozygous carrier, then inbreeding can give rise to afflicted homozygotes. However, for lab strains, it is actually desirable to use completely inbred lines where all animals are as near to 100% identical (from a DNA sequence perspective) as you can get. This makes genetic mutational analysis far easier (possible).

It also depends on the alleles in question. Not every mutation is purely dominant or purely recessive. You can have situations, such as with some tumor suppressor genes, that diversifying the population by outbreeding to someone with a functional tumor suppressor, will still cause the offspring to have only a single working allele, and therefore an increased probability that they can sustain a random mutation that will knock the working gene out. You can also have cases where having one functional copy of the gene isn't enough, so the offspring are haploinsufficient. You need two doses of both working copies of an allele to display the non-afflicted phenotype, though the afflicted heterozygote has a better time of it that the afflicted homozygote, who has none of the working allele.

You also have X-Linked conditions. If the maternal lineage is inbred, then all of the males will be afflicted and females will be carriers.

Another possibility is that the outside breeder is a carrier of the mutant allele so the offspring remain homozygous or the outside breeder has an allele of the gene that comes with its own defect. They may not be afflicted, as they could be heterozygous for a working copy, but their offspring with the inbred line could be heterozygous afflicted because neither of the alleles they inherit are functional, it is just that they are not functional in different ways.

Sexual reproductions main advantage is that it is supposed to increase diversity in the population and increase survivability of the species. When you have isolated populations or inbreeding by choice, then this can circumvents the benefits. Not all inbreeding, as seen with laboratory strains and selective breeding of domesticated animals, is deleterious. It is just that the breeder needs to be careful of the choices made and cognizant of how the genetics can work. Animals displaying a diseased phenotype should not be allowed to produce offspring, and you need to evaluate the siblings of that animal as well as the parents to insure that you do not have problems in that lineage.