Then he found a loophole in his punishment: Although he couldn't be in the garage area, NASCAR wasn't banning him from track property. And he was only forbidden from using the team's radio communications, but text messaging, cell phones and instant messenger were fine to use.
So Eury called off the trip to Maui and traveled to five of the six races he was suspended from to support driver Dale Earnhardt Jr.
That didn't sit well with chairman Brian France, who has instructed his officials to inform suspended team members they are not permitted to be on track property during their punishments.
The change comes as Eury's suspension ends - he's at Daytona International Speedway preparing for Saturday night's race - but Hendrick Motorsports crew chiefs Chad Knaus and Steve Letarte have five races remaining on their penalties.
"We'll throw the fear of God into everybody and hope they won't be seen at the racetrack," Nextel Cup director John Darby said Thursday.
That's where Eury went wrong.
He was somewhat discreet about his presence for the first four races, but many believe he flaunted it last weekend at New Hampshire when he parked his motorhome on a hill outside the track. He then climbed on top to watch the race in a lawn chair, equipped with his scanner and a laptop computer so he could aide Dale Earnhardt Jr.
"He was parked up on the hill with all the other fans, and I guess there was no real discussions about whether or not he could participate as a fan and come to the race," Earnhardt said. "They never said he totally had to be off the premises. If they had made that clear, we would have definitely worked within their guidelines."
Eury believes France only found out about the loophole in suspensions this past week, and is now working to close it.
"I know he's pretty mad about the whole deal," Eury said. "But we went to the proper people and asked them what the rules were and what they wanted us to do. I just don't think he knew, to be honest. Brian didn't know what they were doing."
Suspended crew chiefs have been suspected of showing up at race tracks for years.
They could set up shop in a motorhome to be on hand to assist their driver and team. They could offer advice on setups, pore over practice data and counsel the crew on strategy. And although they weren't on the pit box to make the split-second decisions on race day, they were close enough to offer opinions.
Earnhardt said that's all Eury was doing, and it was the same support Eury could have provided from his living room.
"We were going to utilize him whether he was at the track or not," Earnhardt said.
NASCAR knows that, which is why series officials were somewhat lenient with the enforcement of the suspensions. They have no way to keep the crew chiefs out of the grandstands, the infield or the luxury suites, and they have no way of preventing them from communicating in some way with their team.
Where: Daytona International Speedway in Daytona Beach, Fla.
When: 8 p.m. Saturday
Track dimensions: 2.5-mile tri-oval with 31-degree banking in the corners
Television: 7:30 p.m. TNT
Last year's winner: Tony Stewart