The first time Shinichi attended a heist as himself (not counting the clock tower) was exhilarating. Being able to work (somewhat) with the Task Force had been much better than sneaking around trying not to get kicked out or dragged away by Ran. And working with Hakuba Saguru had been enjoyable; they'd played off each other amazingly well. With Shinichi's ability to predict KID and Hakuba's experience working with the Taskforce, they'd nearly cornered the thief. It didn't occur to him until days after the heist that he'd never worked with Hakuba as Conan when Suzuki Jirokichi had challenged KID to steal from him.
…Why had Hakuba never attended one of Advisor Suzuki's challenge-heists? It seemed odd, and slightly suspicious, that the detective most well-known for chasing KID had never been involved with those heists. If it were merely circumstantial, he would have attended at least one of them, and Conan had never seen Hakuba at a heist.
He couldn't have been in London during all of them. While the timing between Suzuki's challenges was erratic and somewhat unpredictable, there were always speculations in the papers for days before the heist. Suzuki always made sure his challenge and KID's response were in the news; publicity is the point of the 'battle for the front page' he talks about as his reason for the challenges in the first place. KID usually sent his answer to the challenge a day or two before the actual heist, and Suzuki's challenges were in the paper for at least a day, sometimes as much as a week before KID sent a response. If being in London had been the only barrier, Hakuba could easily have caught a flight back to Japan when Suzuki sent out his challenge and been back in plenty of time to attend the heists.
Was there someone trying to prevent Hakuba from attending the heists? Advisor Suzuki doesn't like sharing spotlight, so antagonizes detectives (as seen by his arguments with Nakamori and Kogoro) but he didn't mind Conan's presence. Hattori and Kogyoku-san have both been involved with the challenges, so it's unlikely Suzuki would prevent Hakuba from attending. He'd heard the Task Force wasn't welcoming of Hakuba at first and he still goes after KID, so arguments or put-downs from Suzuki would be unlikely to have a large enough effect to make Hakuba avoid a heist.
KID was the only other person Shinichi could think of who possibly might try to keep Hakuba away from the challenge heists. Even if the thief disliked Hakuba, preventing him from attending heist seemed unlikely. Prank him or otherwise incapacitate him during a heist, definitely. But keeping him from attending altogether seemed out of character. It also seemed unlikely when the tricks KID pulled when he was challenged tended to be more elaborate (and require more preparation). If KID didn't want Hakuba interfering with something at the heist it was much easier for the thief to wait for Hakuba to arrive and ambush him. Even if, for some reason known only to the thief, KID didn't want Hakuba to attend heists with Conan, it would be the same—easier to ambush him at the heist before he ran into Conan. If something like that had been happening, Shinichi would have heard about it after one of the heists.
Is it there something about the heists themselves that would cause Hakuba to avoid them?
KID seems to pull flasher magic tricks (maybe for the fans? Putting on a larger show for the insane audiences Suzuki attracted with his publicity stunts?) But as a detective Hakuba probably wouldn't care, it's just a larger or more difficult trick to solve.
So it's probably not KID's tricks. Advisor Suzuki tends to come up with complex and strange security measures (but then so does the task force). Hakuba is smart and could easily work around whatever it is to go after KID.
Was it for personal reasons?
Hakuba mentioned that he has a primary suspect, so he's convinced of KId's identity. He's known for chasing KID, wants to know why he steals...
! He doesn't care about the challenge heists because KID was baited?! They're all instigated by Suzuki, so (theoretically) have no bearing on why KID became a thief in the first place. It's possible KID takes Suzuki's challenges more as a performance than other heists, and only steals the jewels for the showmanship (and possibly to defend his title or something similar).
So, Hakuba might avoid the challenge heists because they could potentially skew his data about KID's motives and lead him to incorrect deductions. But detectives need to take into account all possible data and clues before coming to conclusions. Even if KID isn't instigating the heist, he still goes to steal the jewels, and it's possible his methods or words during the heist could give hints at his hidden motivations.
Is Hakuba purposely limiting himself? By avoiding the heists where KID usually pulls his largest and flashiest tricks, and is potentially distracted enough to let something slip by accident, Hakuba is forced to work with limited observations, and only what clues KID feels inclined to give.
…Was that the answer? Hakuba didn't want to catch KID, or discover the thief's motivations, because of a potential slip-up on KID's part. Possibly he wanted to convince KID's civilian identity to reveal his motives on his own. But then why continue at KID's usual heists if he no longer prioritizes catching the thief? Hakuba didn't seem the sort to care if the media spread stories about him no longer chasing KID…
The snipers. Hakuba had found out about the snipers and wanted to make sure KID didn't get hurt. It was also possible he'd been looking for a chance to catch them. And there had never been reports of gunshots at one of Advisor Suzuki's challenges to KID. Possibly because of the publicity; the snipers were much more likely to be discovered (and caught) when the constant coverage in the papers had every KID fan who could get to the location swarming anywhere around the heist location that might give them a glimpse of KID.
Therefore, Hakuba didn't attend the challenge heists because he had no reason to do so. He was attending heists in order to catch the criminals attempting to murder KID, while trying to convince KID's civilian identity to either share his motivations or stop holding heists altogether and let the police deal with his attackers.
Shinichi doubted that his fellow detective would convince KID to stop holding heists. Catching potential murderers however, was definitely something that interested Shinichi. It seemed he would be attending KID heists more often in the future.