If you have the nutrio upgrade segment, it disables DNA degradation completely.
My kubrows didn't lose loyalty since yesterday. I think not having a kubrow or kavat in your active loadout (edit: or in any loadout) prevents the loss of dna integrity and loyalty, but I can only test loyalty since I have the upgrade.
Edit: I've put my Sahasa in one of my loadouts and Sunika in another, and now the Sunika is roaming in my ship and using the incubator allows me to see its stats. Switching to the loadout with Sahasa causes it to roam the ship, but the incubator shows me Sunika's stats. After a mission or relogging, it reverts to showing Sunika roaming, even though the Sahasa loadout is selected. I'll have to wait until tomorrow to see which one's loyalty goes down, but I suspect it'll only be Sunika, since that one seems to count as being out of stasis.