Here are two theories of divine conservation, tendentiously labeled:
Occasionalist conservation: That a creature that previously existed continues to exist is solely explained by God’s power.
Concurrentist conservation: That a creature that previously existed continues to exist is explained by God’s power concurring with creaturely causal powers (typically, the creature’s power to continue to exist).
It is usual in classical theism to say that divine conservation is very similar to divine creation. This comparison might seen to favor occasionalist conservation. However, that is not so clear once we realize that classical theism holds that all finite things are created by God, and hence creation itself comes in two varieties:
Creation ex nihilo: God creates something by the sole exercise of his power.
Concurrentist creation: God creates things by concurring with a creaturely cause.
Most of the objects familiar to us are the product of concurrentist creation. Thus, an acorn is produced by God in concurrence with an oak tree, and a car inconcurrence with a factory. (The human soul is an exception according to Catholic tradition.)
Because of this, even if we opt for concurrentist conservation, we can still save the comparison between conservation and creation, as long as we remember that often creation is concurrentist creation.
Which of the two theories of conservation should we prefer?
On general principles, I think we have some reason to prefer concurrentist conservation, simply because it preserves the explanatory connections within the natural world better.
However, if we insist on presentism, then we may be stuck with occasionalist conservation, because presentism makes cross-time causal relations problematic.
[Edited Nov. 4 2020 to replace "cooperation" with the more usual term "concurrence".]