The phrase "alert for some time" is correct and usable in written English.
It can be used to describe a state of being vigilant or watchful over a period of time.
Example: "The security team remained alert for some time after the alarm was triggered."
Alternatives: "vigilant for a while" or "watchful for a period".
"And I think we're going to remain on a high state of alert for some time".
Our military forces and our embassies in the region have been on heightened state of alert for some time now.
Mr. Rosenbaum was alert for some time after the stabbing, but at Kings County Hospital Center, the State Health Department determined, doctors failed to notice a four-inch-deep stab wound for nearly an hour, and he bled to death internally.
The wearable features Polar's Smart Coaching via the Android wear app, along with standard fitness (no stair count, however) and sleeping and features the inactivity alert the company has offered up for some time.
When it comes time to encounter your housemate, be alert for the next time they say something that rubs you the wrong way.
The center issued a "particularly dangerous situation" alert for the first time since June 2014, when two massive EF4 twisters devastated a rural Nebraska town, killing two people.
Temperatures in parts of the country have hit record highs, prompting an emergency level-two nationwide heat alert for the first time.
Temperatures in parts of China have hit record highs, prompting an emergency level-two nationwide heat alert for the first time.
The announcement was unusual for Drupal and left developers on high alert for the targeted time frame of the release on Friday.
Or should we blame the South African military, which transformed a minor event into a national scandal by putting all its bases on high alert for the first time in its democratic history?
