Products that kill the weeds will kill the desirable plants. Preen works by interrupting seed growth. Established plants are not affected. Unfortunately there is no easy solution. You can dig each bad plant out or spray the bad ones with something like roundup (being very careful not to touch the good plants). Or if there are more bad than good, take out all of the gazania, spray all of the bad plants being careful not to spray the woodies, then replant the gazania plants.

There are some of these plant poisons that have been removed from the market because it was found that they could kill desireable plants when the stuff reached those plants roots. Desireable trees and shrubs have been killed after these products were applied. A neighbor sprayed a 2,4,D product a few feet from one of my Lilac shrubs, years ago, and it still is not growing like it did before then. Every plant poison has undesireable affects on our environment despite what the manufacturers of these products tell you.
The best method of controlling unwanted plants ("weeds") is to remove them by hand, mechanically.

My "technique" is to judiciously:

Hand-pull every weed and their roots.

turn the soil and remove any remaining weeds, roots and other weed parts.

rake the soil to level it out.

apply a 5 lb. container of Preen Garden Weed Preventer, per its application instructions.

water the garden, by an automatic sprinkling system, for less than 20 minutes every two nights

But, in spite of this work, new new weeds sprout within two weeks.

If I repeat my "techinque", how can I prevent new weeds from growing?

You can try using 4 or so sheets of newspaper torn to fit around desirable plants on top of the soil then mulch on top to hold it down. This always works for me.

How do I fit the newpaper around the gazania groundcover?

More than likely the new "weed" growth within two weeks is from new seeds and not regrowth from the previous plants, so you either have a lot of these seeds already in your soil or there are plants somewhere producing seeds that are being deposited in that bed. Controlling "weed" growth in a bed with a ground cover growing in it can be difficult because any plant poisons will also kill the ground cover and placing newspaper or cardboard is very difficult, as is any other type of mulch.
There is a bed of Ivy that had a problem with Nightshade growing in it that I finally did pull all of the Nightshade roots from several years ago and have since kept new growth of Nightshade pulled, but this is an ongoing job since birds eat he berries Nightshade produce and drop the seeds in those berries which then grow into new plants.
This may well be one of those jobs where you need to spend and hour or two a month doing.

I have read the best thing to do is hand pull the weeds and then put plastic down. Just did this myself.

"turn the soil and remove any remaining weeds, roots and other weed parts.

rake the soil to level it out."

This technique is bringing NEW weed seeds to the surface, which sprout and grow.

Use a scuffle hoe (hula hoe) and just slice out the new ones, or surround your desirable plants with a shield of some sort and carefully spray them with glyphosate.

" then put plastic down."

I'm sorry to say that plastic has NO place in a garden!! Landscape or weed fabric is bad enough but plastic is even worse. It prevents gas exchange via the soil surface and inhibits adequate water penetration from rainfall or irrigation. Plastic can seriously stunt plant growth and in extreme cases, even kill them.

Manually remove all the weeds then apply a decently thick layer of mulch. That will keep weeds at bay but not from never returning.........weeds are a gardening fact of life. But if they are dealt with when they appear, they will be far less of an issue.

An application of a pre-emergent herbicide can help as well. This will prevent new weeds germinating from seed or the seeds developing properly but will have no effect on any existing weeds (therefore the need for complete removal) or on any desirable plants. It only affects seeds or seedlings.