Well - my thought is that this all depends on what a "cycle" means. If you mean that they burn a different area each year, then I think the colony will be OK. If they burn the whole lot, then not
Quite a few species benefit from rotational destruction of a fraction of their site, since it often allows overgrown areas to be cleared and "new life" to subsequently emerge. Coppicing would also fall into this category - even giving the Heath Fritillary the nicknake "The Woodman's Follower" as it moves into areas recently coppiced!
Cheers,
- Pete