Harry isn't looking for Thomas in Small Favor because he's off pretending to be Harry most of the time; he's looking for him in the next book, Turn Coat. Harry uses Little Chicago shortly after Mab messes with his head, to send the Gruffs on the wild goose chase with Mister's help, so I don't think they could've removed that. What led him to the island was Nicodemus setting the meet there.
There's no real need to use Little Chicago in Turn Coat; Harry finds out that Thomas is missing, gets the lead from Vince Graver, follows it directly to the lawyer, soulgazes her, finds out that the White Court was involved, and heads to see Lara with Luccio. That's when the Skinwalker tells him that he's got Thomas, and gives him all the contact information he needs to set a meeting later on. He mentions that it would be near impossible to find the skinwalker with magic as a handwave, and has Lara try to trace the cell phone instead. Meanwhile, Harry's balancing dealing with Morgan and keeping him alive while finding the traitor. Little Chicago would just have taken him valuable time (I recall it taking him something like an hour or two to get ready to use it each time) when he's got other stuff to do.
I'm not saying it's totally impossible, but that the motivation and means behind it is sketchy, in my opinion.
I was incorrect about the timeline of events, yes. The original theory I was referencing is by Ms Duck, has a "Strong Evidence" label on theories list, and can be found
in post 2 here.
Small Favor
Now this is where life gets interesting. Mab outright (she admits it) takes Harry’s blasting rod and then makes him forget she took it. What she leaves behind is the image of a tarp, and a splitting headache. SF 212:
Quote
“pain stabbed into my head, ice picks plunging into both temples. I flinched and doubled over. Blasting rod. Familiar words. I fought to summon an image of what went with the words, but I could not find anything. I knew the memory associated with those words, but try as I might, I couldn’t drag it out. It was like a shape covered by some heavy tarp…”
The second thing that happens in this book is Harry meets the isle for the first time. There is also a small in-joke here; when researching gruff, harry find a Calvin and Hobbes book. For the non fans, the last strip of the comic had Calvin ( the too bright smart alleck) and Hobbes ( his wiser but snarky and horny friend only he can talk too) head off into a eternal winter wonderland of snow, magic, and snow goons. (yes, Mab left him a book)(that has a beware of Hobbes in joke)
Turn Coat and the two clue bats:
The first clue is on page 211
After Thomas is taken, Harry searched for him magically, but never uses or mentions Little Chicago. (although damaged in WN, it is fixed by this time, note SJ).. all he describes is:
Quote
“a long table in the center of the room is covered by a canvas tarp.
.
Now it is important that not only does he not mention it ( he does in every other book, whether he uses it or not, he is very proud of it.) but Bob does not mention it either. And almost the very first thing he mentions in the books is his splitting blinding headache.
The second clue is on page 215
Mouse come over to talk to him, gets Harrys attention, and then when Harry bends down, harry gets a second blinding headache, and loses his train of thought. This is important because it is shown later that Mouse could have found Thomas, and he certainly believed he was a match for shaggy, or at least that harry and he together were.So someone covered the table, removed the memory from Harry and Bob, and gave Harry a headache just in time to prevent him from rescuing Thomas.
Why would Mab do this?
Two possible reasons: First, she believes Harry and Mouse were not a match for shaggy, or she needed Harry to bond with Demonreach for another later purpose, and Thomas being in trouble was the goad she used to get harry to do something this drastic.
The clue bats she is referring to are a WoJ about two hidden clues in TC:
The clue bat is a tough thing to guesstimate. I mean, I hit y'all with at least two other major things in this book that no one seems to have picked up on at all, so far. 
What is relevant to our specific discussion here is that Bob was in the room with Harry, helping him go through tracking spells in the lab, trying to find Thomas, immediately after he learned of his capture by Shagnasty:
Two hours and a half a dozen attempted tracking spell later, I snarled and slapped a stack of notepads off a corner of a table in my sub-basement laboratory. They thwacked against a wall beneath Bob the Skulls's shelf, and fell to the concrete floor. "It was to be expected." Bob the Skull said very quietly.
So he did put time into trying to find Thomas with magic, but neglected to use his single most valuable tool for this sort of problem. He doesn't even mention it as an option, or even acknowledge its existence while running down a description of the room. Ms Duck points out how out of character that is, Harry is immensely proud of LC and name drops in every other book it exists in. And it is just as odd that Bob doesn't suggest using it, it's had quite a few successful outings by now. So why not?
Restating my theory with the proper timing, I think Mab has influenced / made a deal with Bob, Bonnie, and/or Id Harry by this point, agreeing to nudge Harry toward Demonreach in exchange for hiding Bonnie's existence from Harry for now. And if Bob was in on Bonnie's existence, it paints his request for a backup vessel in a whole other light, doesn't it?
One more stray piece of evidence, Harry's intuition (aka Id Harry) is the one that comes up with the idea to take Morgan to Demonreach, after brainstorming with Murphy in TC Chapter 34.
