Naive reasoning suggests that a string theory vacuum with cosmological constant Lambda1 is always unstable as long as there is a string theory vacuum with cosmological constant Lambda2 < Lambda1 since the later is a state with lower energy density. If it's true, there should be very few stable vacua since these would be the vacua with the lowest possible cosmological constant. These vacua would probably have a Planckian-size cosmological constant and therefore be highly non-classical.
However, I suspect there is something wrong with this line of reasoning. Probably I am thoroughly confused about something.
Also, how to compare stability of vacua with different number of large dimensions? Comparing cosmological constants doesn't feel to make sense.