Why do I get slightly different results every time?

${\mathfrak{A}melia}$ uses random simulation to create multiple imputed datasets. This is not a compromise, and it makes computations easy that would otherwise be impossible. If you need more precision, increase _AMnds. If you really want exactly the same numbers for each replication, set the Gauss random number seed with the Gauss command rndseed before running ${\mathfrak{A}melia}$.

Like every numerical optimization algorithm, the EM stage of the algorithm can sometimes settle on a local rather than a global maximum. You could try different starting values for the theta matrix of sufficient statistics using the global _AMstart in amelia if this seems likely.