Unless the mission is short --Alcubierre FTL, with 'Double Bubble' to avert need for anti-matter fuel and oodles of hull Unobtanium ??-- you have the twin issues of keeping a 'restricted' population 'focussed' for several generations, and getting there before an FTL ship can be devised and built...
There's a grim caution about familial commitment, "Clogs to clogs in three generations..."
https://en.wiktionary.org/wiki/clogs_to_clogs_in_three_generations
There are many versions of this admonition, all scary...
SciFi provides us with generation-ship collapsing to illiterate savagery, 'Non-stop' by Brian Aldiss.
"Captive Universe" by Harry Harrison, has two genetically engineered clans, isolated by a lethal robotic river monster and a grim religion. They'll stay 'sheeple', dull peasantry, for generation after generation until ship arrives at destination. Then they'll be bid inter-marry, which will un-lock their genes, birth bright kids...
The classic line in 'Dune' that "Institutions Endure" carries weight, here. Snag is institutions may become toxic, spawn heresy or suffer 'palace coups'...
Tangential, consequent loss of skills may doom mission. IIRC, the Byzantines' recipe(s) for 'Greek Fire', their 'Ultimate Weapon', was so closely held that crucial parts were lost to purges and/or coups. Yes, yes, some 'counters' had been developed, mitigating GF's efficacy, but...
Think how eg Coca-Cola or KFC reportedly stored their recipes like a jigsaw puzzle, with different parts in different places. Even with 'paranoid' redundancy, 'Dire Lord Murphy' may strike...
IMHO, modern analogy to Byzantines' loss of 'Greek Fire' would be the US nuclear weapons program discovering they could not make fresh 'FOGBANK' aerogel spacer for new H-Bombs. The old, reliable recipe simply did not work any more. IIRC, this was eventually, expensively established as due to '
modern' reagents being '
much too pure', lacking some vital trace of nigh-catalytic [REDACTED]. IIRC, polyethylene manufacture was initially thwarted thus, resolved by discovery that a trace of oxygen was needed to initiate polymerisation. More reliable catalysts were devised...