This is one of the most important things to understand about pet insurance, so here is a clear answer.
As long as you renew your policy on time each year without a break, an ongoing condition that started while you were covered can continue to be considered at each renewal, up to your annual limit for that year. Your cover does not simply stop because a condition became long-term.
Two things to keep in mind:
The one thing to avoid is letting your policy lapse. If there is a break in cover, that condition would then be treated as pre-existing when you come back, and it would no longer be claimable. So if your pet has an ongoing condition, keeping your policy continuous is the most important thing you can do.