The phrase "a steady search" is correct and usable in written English.
It can be used to describe a continuous and persistent effort to find something or seek information.
Example: "The detective conducted a steady search for clues that would lead to the resolution of the case."
Alternatives: "an ongoing quest" or "a constant pursuit".
A steady stream of filtered search terms and propaganda directives guided coverage and discussion of a broad variety of topics and stories, from Xi Jinping's steamed bun meal to the arrest of former security chief Zhou Yongkang.
In fact, looking at Google web searches from July 2011 to July 2013, a nearly identical "M" shaped interest curve can be seen, with an initial burst of searches, a steady decrease, then a second burst of interest approximately a month later, followed by an exponential decrease in attention.
Since September of 2017, there's been a steady increase in people searching "astrological compatibility".
Some of today's servicemen and women volunteers may have joined in search of adventure, but many more did so in search of a steady income and the hope of acquiring the tools of a future civilian job (a major selling point for recruiters).
That may have prompted her to publish several books in quick succession, perhaps in search of a steady patron.
A retired couple in search of a steady income should not put their nest egg into a fund that invests only in volatile tech stocks or high-risk emerging markets.
Once the preferred path for carrying rich Zanskari butter to trade in Leh, Ladakh's main town and an old hub on a spur trail of the Silk Route, the Chadar still carries a steady traffic of Zanskaris in search of work, goods or an education at distant schools.
He went through work, traveled the world, did menial tasks and odd jobs, all the while in search of a steady income that would ensure his wife, children and siblings were given the best upbringing possible.
