"continue to be unable" is a grammatically correct and usable expression in written English.
You can use it when referring to a situation where somebody has been unable to do something and is expected to remain in that state. For example: "Even after months of trying, she continues to be unable to make progress on the project."
He said that, unless vaccine prices come down, developing countries would be continue to be unable to pay for them.
Unless measures are taken to reverse this defect in our system, we will continue to be unable to correct access and cost problems.
"If Congress and the White House continue to be unable to get anything done," said Lisa Shalett, the chief investment officer at Merrill Lynch Wealth Management, then "we are playing with fire".
However, he also sought to assert the necessity for Pinewood's increase in capacity, by saying: "Although we have hosted the three largest film productions of the year, being Star Wars: Episode VII – The Force Awakens, Avengers: Age of Ultron and the 24th Bond film Spectre, we continue to be unable to meet all the demand from large films.
Though in Q3, gross domestic product for the 16 countries using the Euro grew by 0.4% from the second quarter, according to Eurostat, many residents continue to be unable to secure work.
If they continue to be unable to register new players and their best players leave during administration, manager Gary Locke will be hard pressed to field a team capable of staying in the top league, especially with the points penalty.
The pair was first up against The Miz and Damien Mizdow with the former Tag Team Champions continuing to be unable to co-operate.
"The food industry continues to be unable to come to grips with the health risks associated with potentially fatal food allergies".
The Obama administration's report to Congress on Pakistan states, "As a result of political gridlock, the government continues to be unable to develop consensus on difficult economic and fiscal reforms that are urgently required, including systemic tax reform".
Previously, Mr. Allen and the union president, Alan Rosenberg, planned to ask union members to approve a measure that would allow a strike to be called if negotiators continued to be unable to reach an agreement with the producers' group.
Both of these problems, needless to say, will be exacerbated if Romney continues to be unable to talk about his wealth in anything save the most clueless and flatfooted fashion.
