I don't know if they reset perks/traits for Fleet Admirals upon gaining a new level/spec point but I don't think this is the case.
I recently overhauled my characters' skills (allocating pooled spec points, re-selecting traits, etc.). 2-3 days later (today) one gets a promotion. I click the skills menu to add the point and the character has NO traits OR perks at all... other than 2 starship perks, which makes the whole thing even more baffling/buggy.
Whether intentional or not I now have a new task to obsessively monitor amongst the other 150.