The phrase "a willingness to keep" is correct and usable in written English.
It can be used when discussing someone's readiness or openness to maintain or continue something, such as a relationship, commitment, or practice.
Example: "Her willingness to keep the lines of communication open has strengthened our partnership."
Alternatives: "an eagerness to maintain" or "a readiness to continue".
Consumer confidence, or at least a willingness to keep spending, with very low interest rates, has been a vital element of keeping the economy growing over recent years.
He has a doggedness, a willingness to keep going day after day, whatever the setbacks.
But I believe European leaders should themselves express a willingness to keep the door open.
Both sides indicated some flexibility and a willingness to keep talking.
(Nor is there much of a willingness to keep quiet, to help the other side look good).
"Show me the third room first," this woman says at check-in, telegraphing a willingness to keep at it until she's offered a room she likes.
When the attackers turned out to be those of a warlord, not the Taliban, some concluded the U.S. had a new willingness to keep peace itself -- an idea the U.S. promptly rejected.
But that has changed, as studios took advantage of faster digital production techniques, and showed a new willingness to keep pace with the increasing pace of the media world.
"Yet without one combat casualty," The Times continued, "the American-led NATO alliance has proved Mr. Milosevic wrong... his government has unwillingly become the first case study in how precision weaponry, overwhelming resources and a steely willingness to keep bombing can compel victory -- all without risking soldiers on the ground".
Instead, there is an unbelievable willingness to keep the thing as a series of new questions.
Like Monksfield, Hardy Eustace was a grafter whose willingness to keep scrapping helped him to see off flashier types when defeat had seemed certain.
