Washington (CNN) The dustup over a White House aide's crass remark about Sen. John McCain's health has once again inflamed the White House's frustration with staffers who reveal the inner workings of the West Wing to reporters outside the building. Despite active efforts to flush out administration leakers -- including machines used to detect unauthorized cell phones in the West Wing -- President Donald Trump and his senior aides haven't yet been able to stem the flow of damaging information.

Deputy press secretary Raj Shah was in the daily communications meeting with about two dozen other officials last week when Kelly Sadler, a previously little-known aide, remarked that it didn't matter that McCain, an 81-year-old, six-term Republican senator with brain cancer, opposed the administration's pick to lead the CIA because "he's dying anyway."

Asked about the remark Monday, Shah reiterated that the White House's internal frustration over the episode was that it was leaked. He focused on the leak itself rather than the content of the remarks in his exchange with reporters.

"If you aren't able, in internal meetings, to speak your mind or convey thoughts or say anything that you feel without feeling like your colleagues will betray you, that creates a very difficult work environment," Shah said from the podium in the briefing room Monday. "I think anybody who works anywhere can recognize that."

But many of Shah's colleagues inside the West Wing see the leaks of information as impossible to prevent. Dozens of senior officials speak to reporters on a daily basis, including, at times, Trump himself, and White House efforts to prevent leaks have fallen flat.

Unprecedented steps

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The White House banned the use of personal cell phones in the West Wing in January. It was an idea first floated by chief of staff John Kelly when he replaced Reince Priebus last July, but one he didn't implement until months into his tenure. Officials publicly maintained that the ban was because of national security reasons, but multiple staffers said privately that they were under the impression it was carried out in hopes of limiting leaks to reporters.

Kelly was agitated when a memo he wrote outlining the new policy quickly leaked to media outlets, a source familiar with his reaction said.

Though the ban prompted widespread frustration among staffers, most abided by it, simply because there wasn't an alternative. How the phone ban is carried out was described to CNN by four White House officials who spoke on the condition of anonymity. The White House declined to comment.

Officials now either leave their personal devices in their cars, or, when they arrive for work each morning, deposit them in lockers that have been installed at West Wing entrances. Each locker has a key, which officials said take a little jiggling to remove. The staffer puts their phone in the locker, locks it and hangs on to the key until the end of the day when it's time to reclaim their device.

Sources said it's common to find several staffers huddled around the lockers throughout the day, perusing their neglected messages. The lockers buzz and chirp constantly from 6 a.m. to 8 p.m. Monday through Friday.

The ban isn't based on an honor system. Sweeps are carried out to track down personal devices that have made it past the lobby and into the building. According to sources who are familiar with the sweeps, men dressed in suits and carrying large handheld devices have been seen roaming the halls of the West Wing, moving from room to room, scouring the place for devices that aren't government-issued. If one is detected, one of the men will ask those in the room if someone forgot to put their phone away.

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In the early days of the ban, staffers would forget, or didn't realize that the ban included Apple watches. But if no one says they have a phone, the men begin searching the room.

The devices are largely accurate, sources say, and can even determine what type of device is in the room. When the ban was first implemented several months ago, a group of lawmakers was waiting for the President in the West Wing while a sweep was being carried out. The device picked up a Samsung Galaxy, which was in the pocket of one of the visiting lawmakers, according to a source familiar with the situation.

In his memo outlining the policy, Kelly warned that anyone who violated the phone ban could be subject to disciplinary action, including "being indefinitely prohibited from entering the White House complex."

But several staffers later remarked that they don't actually believe anyone would be fired for violating the policy, with multiple noting this week that the ban did not prevent Sadler's comment from leaking to the press.

'Traitors and cowards'

JUST WATCHED Trump: WH leakers are 'traitors and cowards' Replay More Videos ... MUST WATCH Trump: WH leakers are 'traitors and cowards' 01:22

Trump has frequently blasted leaks coming out of his White House and has long believed that there are individuals inside his administration who are actively working to undermine him. He tweeted Monday that embarrassing stories about his administration that are based on leaks are a "massive over exaggeration put out by the Fake News Media in order to make us look as bad as possible."

"With that being said, leakers are traitors and cowards, and we will find out who they are!" he wrote.

Counselor to the President Kellyanne Conway said on Fox News Monday evening that she spoke with Trump about the leak issue multiple times that day.

"There are all kinds of leaks," Conway said. "Some leaks exist to hurt colleagues, some leaks exist because they disagree with the policies that are being put forth. But none of them are helpful and I will tell you something else that's going on in this White House, but not as badly as it was in the beginning, it's not so much leaking as using the media to shiv each other."

She was asked if she expects personnel changes in light of the latest disclosure.

"I do, actually. Yes, I do," Conway said.

CLARIFICATION: This story was updated with additional context about Shah's comments Monday.