Oops! Sorry about that. I thought there was a possibility puzzles with the space not on an edge/corner may have issues, but I wasn't sure. Do you know if the one you managed to solve had a mid-field space?
No, the board is randomized by swapping random tiles. I'm pretty sure now that all puzzles are solvable, though mid-board spaces do add a little extra mental barrier. I've run into 2x2 grids that I can't get but then a friend solved them very quickly, so I think there are just little niches our brains end up in that we can't shake out of. I might be wrong though!