Those insects are around us all the time, but we often do not see them since they really only become a problem on our plants when they become stressed, or are growing unhealthy.
A good, in depth look at the soil these plants are growing in, now, is a good idea. What is your soils pH, what nutrients are there and are they in balance?
How much organic matter is in the soil?
How well does that soil drain?
How well does that soil retain moisture?
What kind of life is in that soil?
Taking steps now to create a good, healthy soil that will grow strong and healthy plants will help next growing season.
Some people suggest cleaning up all plant debris from the garden to remove any potential hiding places for the pests which also removes winter cover for any beneficials that might want to stay put too. Since pyrethrin based dusts and sprays are very broad spectrum they need to be used with great care so they do not poison the beneficials. The Piperonyl butoxide is used to enhance the activity of the pyrethrin, I'm not sure why it would be necessary.

Thank you for your reply.
Actually, I did a thorough aerating and conditioning of my soil in the spring with Dr Earth probiotic organic flower garden fertilizer, and if it weren't for the thrips my garden has never been healthier. The flowers would start to bloom profusely then shrivel immediately, and I could see the thrips all over everything (except the marigolds). I could tell the plants were not inherently sickly - just struggling against the thrips. I'm wondering if they weren't brought in from the garden store on the petunias, since that's where I first noticed them after a heat spell. Then they got to nearly everything else.
I could live with the annuals shriveling up, but when they got to the bearded iris and clematis I was really unhappy, as I've been nurturing those for years - especially the iris.

The Garden Safe insecticide would keep the numbers of them down for a while, but they'd come back, and I hated to keep spraying. I'm really hoping that they won't survive the winter (?) or that there is something I can do to prevent their re-emergence.

Since most all organic fertilizers need some time to actually become available to plants, they require the Soil Food Web to do that, putting "fertilizers" on a garden in the spring at the beginning of the growing season is not the best time. Now is the time to prepare your garden for next spring, especially if the soil needs some adjustment to the pH.

Ah, that probably explains why the plants themselves looked so vigorous by mid-summer, despite the thrips.
But I'm still wondering what to do about preventing a return of the thrips next spring, if they live through the winter in the soil or in the roots or remaining parts of the perennials?
thanks much.