Brown can still get back in the Senate. He's got a lot of cash and Wall Street behind him. He won't be going up against a very popular Elizabeth Warren next time. It is just not worth the risk.
Nothing in that HuffPo article says Ax told Kerry to tone it down. On the contrary, it says Ax basically complimented Kerry for getting under Obama's skin. Obama getting "pissed" or letting Romney "get under his skin" wasn't the problem in the first debate. Romney didn't attack Obama as much as lie his ass off, suddenly claiming he was a moderate. The first debate was horrendous because Obama did not firmly call Romney out on his lies. As Obama admitted, he was just too polite. Just like when Kerry didn't call Bush out on his lies while being swiftboated.
I think the reason Ax looked so devastated in the spin room after the first debate was that he realized Obama prepared for a Romney attack, which never happened. Instead, they got Moderate Mitt, and his blatant lies and 180-degree flip flop on taxes on the rich. And Kerry is infamously unable to respond to blatant lies, so I'm guessing his debate prep sucked in that regard.
Beating Bush in a debate is not exactly a huge achievement. Worse, even though he won on points, Kerry just couldn't get a big enough majority of Americans behind him so that the Ohio shenanigans didn't matter. Kerry just doesn't have a whole lot of charisma or likeability, something a Secretary of State could use.