I just had the most surprising event when I got a notification of my only female Labrador getting pregnant as I knew she was already pregnant. I open the animal screen and see there is a puppy literally just 2 hours old. I mean, just how long ago does a animal need to have given birth to get pregnant again. I have even given them free roam across my entire map except the food storage.
I do not think there is a lockout against getting pregnant again.
It is also not Randies choice when a Animal gets pregnant.
They do it.
They get pregnant
But with most timed health conditions, you only are informed when it has been running for a while.