Jimmy was previously always out first because he was the Listeners' chosen back in Evo, over Martyn.
Initially the two of them joined 3L on a mission to stop the Watchers. First the Watchers tried tinkering with their memories to make them forget their original goal of stopping the game, but then the Listeners broke through with Jimmy; so the Watchers had to kill him early to make sure he couldn't interfere.
A cycle that continued again and again. Jimmy joins a Life game as a Listener agent, his memories get wiped, the Listeners call to him and he remembers again, the Watchers eliminate him.
Eventually, after LimL, it seemed as if the Listeners had given up all hope for Jimmy and abandoned him... so for once, there was no urgency to get rid of Jimmy, and he could survive just a little longer. Then WL rolls around, he's genuinely far from first out, and it seems the Listeners might be regaining some faith in their champion.
Which is why Grian, a Watcher, the one running the games, is so intent on getting Jimmy out early again. Enough to assassinate him and let Lizzie be collateral in WL, to casually reference wanting to enforce the canary curse in PL. The Listeners can't be allowed a foothold to meddle in the games again.
That same line of reasoning is also why Martyn's Life Series after LimL is so precarious: before, the Watchers had a strong hold on him, their influence especially heavy in LL (being allied with Grian and Jimmy might have something to do with that); and the Listeners focusing on Jimmy meant Martyn was kinda written off early on.
However, getting so close to a top placement in DL, then winning LimL (albeit under Watcher influence), led the Listeners to decide to focus on him instead. Unfortunately, the Watchers predicted that would happen, so from SL onwards they're making sure to also kill Martyn as much as possible just in case. Grian, being responsible for multiple of his PL deaths and his SL elimination, as the executioner yet again.
TLDR: the Big Property Police Dogs are frequent casualties of a war between Watchers and Listeners, mostly for the purposes of the Grian Empire.