They can be conserved among closely 'related' species, but you have to test their utility. See: Conservation of Microsatellites Among Tropical Trees (Leguminosae)
S. Dayanandan, Kamaljit S. Bawa and Rick Kesseli
American Journal of Botany
Vol. 84, No. 12 (Dec., 1997), pp. 1658–1663.
Another study showed that it is possible to develop microsatellite loci that are both conserved over a broad range of taxa, yet polymorphic within species. See: Conserved Microsatellites in Ants Enable Population Genetic and Colony Pedigree Studies across a Wide Range of Species, PLOS One, doi.org/10.1371/journal.pone.0107334.
They are generally conserved through generations, although loss of interruption within the sequence and occasional germline expansion renders them very unstable and prone to massive expansions from one generation to the next (see the abundant literature on triplet repeat expansion diseases).
Microsatelite sequences can be very well conserved. Though they have the capacity for mutation like most other sequences, there is no special factor that makes them more unstable than several other sequences, except though that some genomic mechanisms that protect integrity of genetic systems may not be very effective on them.
In general, the recurrent mutation remain in the population in low frequency, and that depends on the natural selection intensity against the mutant allele, and may be in another case the mutant allele may have a selection favorable and that factor will assist to increase the mutant allele frequency in the population.