The only way a base can disappear is if it's unregistered, and someone else makes a secret base in the exact same place, or if you delete it yourself.
Also, when you trade records, all your secret bases get transfered. for example:
[John]---|
.............|---[Steven]---[Robert]
[Jake]---|
(don't pay attention to the periods above)
what happens above, is John trades rex with me and so does Jake, so now I have mine, John's and Jakes, and then when I trade with Robert, all my bases go over to his game, so he'll have four, and so will I.
Another cool thing about trading records is that you can
CLONE!
To clone, just trade your team to another person, trade records, trade back pokemon and when you go to their secret base to fight them, they'll have your pokemon, but since to trade back, you have your's as well! It's a great way to level up, because you have equal pokemon, and you already know your own weaknesses, and if you level up your own a few levels before fighting your self, you'll have the edge. I just hope you don't lose to the AI version of yourself...