The phrase "and yet continues" is correct and usable in written English.
It can be used to express a contrast or an unexpected persistence in a situation or action.
Example: "Despite the challenges faced, the project and yet continues to thrive."
Alternatives: "but still persists" or "yet remains ongoing".
It has lost something crucial, and yet continues ("Dogs get used to any loss").
A.I.G. has, of course, received $170 billion in bailout funds and yet continues to incur extraordinary losses — some $62 billion last quarter alone.
"The government recognises that the profession is fragile and yet continues to take grave risks with the stability of the criminal justice system.
"This school continues to tout statistics about its racial, ethnic, and religious diversity and yet continues to make its minority students feel unsafe.
"Europe says settlements are illegal under international law and yet continues to trade with them," said William Bell of Christian Aid UK and Ireland, one of the consortium partners.
Though the plot proves to be as predictable as affairs with married men tend to be, Berne fully evokes every painful step in this one, as when the narrator first realizes that Joseph's favorite words to her are "try, maybe and might" -- and yet continues to hope their relationship will somehow work out.
He called China "almost a police state" and yet continued to welcome dialogue with Chinese leaders.
We know full well that it is causing untold damage and yet continue to pursue and justify it.
In this case, the families "would like to show that the gun companies knew about the dangers of their product and yet continued to market them".
This process could explain, for instance, why an old person's skin can refresh itself with new cells every month and yet continue to look old.
This differs starkly from other cancers, some of which can have survival rates around 90%, and yet continue to receive significantly greater funding.
