"continue to propose" is grammatically correct and can be used in written English.
It is typically used to describe a repeated action or behavior of someone proposing or suggesting something. Example: Despite multiple rejections, John continued to propose his idea for a new business venture to his colleagues.
Nevertheless, economists continue to propose new stimulus ideas with unshaken confidence and over the next six months, the government will almost certainly pass more gigantic programs.
Still, some Texans continue to propose secession to this day.
Agencies continue to propose projects that have environmental concerns and sometimes objections.
But Illinois, Kansas, and Pennsylvania passed their laws between 2011 and 2012 during the current opioid crisis and politicians around America continue to propose new versions.
Nevertheless, proponents for the creationist account of the origin of life continue to propose that it be taught in American classrooms as science.
Across the country, states continue to propose anti-voter legislation that seeks to impose strict voter ID requirements, redraw districts to maintain political power and limit early and absentee voting options.
He followed through, yet, every few years, a member of the Staten Island legislature continues to propose secession.
He signed a bill in 2011 to strip public workers of most of their collective bargaining rights, sparking statewide protests and an attempt to recall him from office, and he continues to propose anti-union laws.
With these handicaps, the influence of conservative ideas in national politics has been confined largely to keeping watch on the congressional liberals who continued to propose most of the new legislation, while conservatives modified or rejected their bills.
Always a good policy wonk, he knows that America's true fiscal problems are the rising costs of health care, not Medicare and Medicaid themselves, but he continues to propose cutting entitlements spending.
While Howard Hughes continues to propose towers that are maximum height, developers are shifting the orientation of many to make them "mauka-makai" (Hawaiian for "toward the mountains-toward the sea") to preserve some vistas for islanders living outside the new buildings.
