He has no clue how to continue? If so white will win, as he has chances on the other side of the board.

At the moment, White is threatening to draw the game by 33.Rxb7ch etc.

NO? What after Qd5, threatening b7? Black must act wisely.

Why not indeed? But the game is still in a state of flux, and could veer sharply either way. White could try 33.b5!? here with the idea 33...Bxc7!? 34.dxc7ch! Ka7 (relatively best - the other two options certainly lose) 35.bxa6! Probably Black would have to abandon defence altogether and shove home his own all-out attack, and hope for the best: 33...h3! 34.g3 fxg3 35.hxg3 axb5 36.axb5 - and now what for Black? 36...Bxc7 is definitely off the table, but nothing else will suffice: 36...Rg7 37.Rc1 and 36....Rc8 37.Rxb7ch!! both lead to a swift quietus. So White had the winning of the game, here, though it would have been by no means easy to find!

A reasonable try, although, according to my analysis in the previous comment, 33.b5 offered the best chance

Rc1 is still a threat: if black plays h3, Rxb7+, KxR, Qc6+, etc. (d7 becomes a threat).

33...h3, all out attack is an alternative. But there doesn't seem to be anything against this move. White doesn't appear to have anything better than to exchange, or allow the exchange.

All that work, but no finish. Well, finding that last combination is a challenge.

I'll have to look deeperly to h3, Rxb7+, but it seems to give white a reasonable counterattack, and if he survives for a couple of moves black's attack, he can recover the piece with pawns and he still has d7. White's problem here is that he missed the best line, and now with the exchange the attack vanishes.

Not much choice in fairness. I don't think black needed to swap though.

I don't agree. Black is defending the right way in order to keep his chances.

Maybe at some point Black could have tried to drive his own attack home with ...h3.

Now white has three ways: 1) Qxa6. It looks fine, but it gives black a tempo, since as long as b6 ans b5 are defended, white has nothing. 2) Qb3+. Nothing happens after Ka8. 3) Rb1. It threats Bxe5+(disc), and after Ka7 (a8, Qd5+), nothing inmediately, but it seems to give white the best prospects. Another story is to analyze black's possible defences or attack (again h3).

Qb5+ looks the only way to keep the d-pawn.

as previously remarked; 40.Qb5ch was essential. After 40.Qb5ch Kc8 41.Rb1 Rxd6 42.Qb3! White can entertain hopes of holding the draw.

That's why Rb1 is to be considered at any time!

Bc3 seems better. I wouldnt want that rook on d2.

This indicates that the game has already swung Black's way.

No. Indications are that 42.Qc4 would have been the best defence, but even then things aren't looking too flash for White. The end should come quickly now, as White is routed all across the board.

(!) White has no more worthwhile counter-attack.

Not even a desperate try like a6 (RxQ, Rb7+, QxR, axQ, Re1#). White has a back rank mate on him, too...

The only choice, in fact. 43. Qc4?? Rd1+ and the queen is lost.

When you starting thinking seriously about 43.Qxe3ch, you know it's all up.

Haha, yes, I did, indeed. No use. No forced repeated moves with checks with the white's dsb and the rook, even if the black king is confined into the a column.

Time to switch to K-side attack: 43...h3!

Yes, the small knife is stronger then the saber here  

Now 44.Bc1! would have been really embarrassing for Black.

Bad try. You can't hope your opponent doesn't see the discovered check and he has a very good place where to redeploy the queen: e4. White's Qc1 threatens the deadly Qc7+, so black has to think how to manage it. It is very interesting, but I have no time to go through it and copy it here. Black has Rc2!, and white must think about Qd1 or Rb4... very wild tactics, here! The point is that even if white is losing, he still has the threat to harass with checks the black king. Until some of this can be kept alive, white can go on playing. But the text move throws away what remained of white's power, even if it defends the a pawn, more important than e4, white is not likely to be able to use it soon.

What exactly is the king defending? Sure looks like he's just watching the show.

I assume the point is that black's king is holding up the passed a-pawn.

Probably defending a6

Isolated islands of resistance remain to wither on the a-file vine, whilst the main Black army surrounds the White King in his stronghold. White has no play left.