Reviving an old-ish thread. I do predator control in NZ and rats are one of my target species.
Where do you put your snap traps? Rodents don't see so well, so given the chance, they like to keep their whiskers in contact with a wall/whatever obstruction they're getting around. If you're not currently, you should move your traps to use that against them.
Instead of baiting a trap and hoping the peanut butter lures them in, skip the bait entirely and put the snap traps perpendicular to and butted up tightly against the baseboard on the outside of your run. When the rat is coming to get its nightly treat it has to run over the treadle plate on the trap.
90% of rodents I catch the first try using this method, no bait - including rodents that just watched another rodent get caught. 90% of the remaining I catch by moving the trap around a corner or someplace new where they aren't expecting it. If those things don't work, then I bait the trap and that works eventually.
If you've been going after this rat for awhile, it probably wouldn't hurt to change the style of snap trap you use, just in case, from the Victor wooden traps to the easy set plastic ones they sell at Mitre10 or Bunnings (or vice versa).
Finally, if that doesn't work, Cacophony Project here has done some interesting experiments and found that a 'leaky' fence is a top tier way to catch predators. Basically they found that predators tended to travel along an obstruction for awhile looking for an easy way through before they climbed over. Using those instincts against them, they erected temporary fencing with, if I remember correctly, warratahs and a plastic sheet like silage wrap. In that sheet they left intermittent gaps and trapped in those gaps using box traps with great success. It wouldn't be too hard to make a temporary leaky fence around your run at least until you catch the bugger. I don't know how readily available box traps are in Oz, but look up the DOC200 if you need inspiration.
Though I hope you caught your menace by now...