Maybe not, but that's because maybe his aura around the players can't be recovered. If it wasn't for this speculation, I'd say yes, absolutely, why not. But because of the players apparently being affected, it may be best to start again with a new voice.
Doesn't reflect badly on Harry's management ability, that's just the circumstances we find ourselves in. Personally I'd rather not take the risk, but that's just my opinion.
Debating on football in terms of whether this manager is good or bad or by insinuating there is a 100% right choice in a game as complex and with as many variables as football is pointless though. Pundits are lining up to criticise SAF for fielding a conservative team against City, even though he usually does it for big games and usually with great success. And you can beat if he 'went for is' and lost 3-0 those same people would be saying he played them too open and should have been more patient in such a big game since they only really needed a draw. It's pointless. They scored a goal from a corner, it didn't happen because of the way they lined up. They may have ended up winning that game 2-0 with that system, they may have lost by more. But it wasn't just because of that system that we lost.
And neither was the decision to loan out Corluka/Bassong/Pienaar/sell Pav the reason we had some bad form. They might have contributed, but really it probably has a lot to do with a million other things too. People saying our fitness training was the problem. We had a great run in when we got 4th the first time, and Harry's fitness methods would have been in full flow then. So was that the problem? More than likely not.
At the end of the day he is clearly a good manager that just like every other manager has to make decisions that with hindsight could look like the worst one. But if he picked the other decision, he may have gotten the exact same result/a much worse result/a much better result. We just don't know. Football is a game with so many variables, with players concentration, luck, the way the wind blows, the way the ball bounces and a million other things that can impact on a result. Harry's a good manager that has been hampered by speculation and doesn't deserve all the insults considering the success he has given us.