I think Grabovski's problem is two fold:
1) Grabovski has lost habits that made him successful - for whatever reason (I'm leaning towards lost confidence or over coaching) Grabovski does not have the shooting instinct that he used to. If you look a large portion of his goals from years passed (see links below this paragraph) they are quick releases or at least aimed at the crossbar. Even that funny little snap/slap shot has completely disappeared this year. Now a lot more of his shots are low and central and he often holds onto the puck too long while aiming. His passing has also seemed to drop off as he doesn't seem as inclined to take risks with drop passes or cross ice passes - the up side is that he usually just skates the puck into the other teams zone and relieves pressure through possession, the down side is that it rarely leads to a clear cut offensive opportunity.
Goals From Years Past:
https://www.youtube.com/watch?v=I691l7c4zXU
https://www.youtube.com/watch?v=k6ZG4JMKHl8
2) Carlyle doesn't depend on him for any particular thing - Many of you are advocating for Grabovski to be moved to another line to get him going, but the sad reality is that Carlyle doesn't need him to score. As someone aptly pointed out, offense is not a problem for the Leafs, it's their defense that could really use tuning. However, Carlyle also has his mind made up about who his defensive role players are. Right now (as in the last 10 games or so) Grabovski is doing well in the faceoff circle, he's getting the puck through the neutral zone effectively (regardless of who he plays with) and his line is not really being scored on. So Carlyle may not be gaining anything by playing Grabovski the way he is, but it's not costing him either, so he's content for now(and if he wasn't my favourite player I probably would be too).
The good news is Grabovski is still skating well, which means the effort is there (and hopefully that there is potential to be the threat he was). A player like Grabovski can be invaluable in the playoffs when injuries set in or the likes of Kadri, Lupul and Kessel start seeing really aggressive checking from the other team's top lines.
As a side note, I keep seeing posts about Grabovski's 5.5 million contract and I get it, we signed him when centres were in high demand and probably overpaid. But I can point to a decent number of higher paid forwards doing far less than he is. Furthermore, Tyler Bozak is going to fetch a lot more than 1.5 million if we resign him so I don't see the value in that comparison in terms of salary. I guess everyone is entitled to their opinion but if we're going to throw Grabovski under the bus because he makes more money than he should, don't you think that bus should have to roll over Dion Phaneuf first?