I'm wondering (although I've assumed this to be true) if Harden's and Howard's personalities were the reason they could never attract that 3rd star to form a true contender. On paper, adding that 3rd star would have made them a legit threat to make the finals.
My memory isn't serving me well, but two big names they've struck out on since landing Dwight are Bosh (who would have been a great fit on paper) and Melo. They were interested in LaMarcus Aldridge and Kevin Love as well this past summer, but obviously didn't work out. Enter Ty Lawson, who I was never convinced would put them over the top, but certainly didn't expect him to fit in this poorly.
Houston will never win a title with Harden and Howard as their 2 best players. They just don't have what it takes.
I think money was why the third star never came. Bosh signed for the 5-year max contract with max raises. Houston could only offer him the four-year max at smaller raises. Given his health issues, that turned out to be a wise move financially.
Carmelo also got a 5-year deal that included a no-trade clause, neither of which Houston could offer. He didn't get the max he could have gotten from NY, but he's still getting more over four years than the Rockets could offer. And since he's apparently unwilling to wave his no-trade clause, we could guess that was an important component of the offer.
Now it could be that if Howard and Harden were more likeable, maybe Bosh or Anthony would have turned down the extra dollars, years, and other security they got from their new deals. We'll never know. But the Rockets were straight-up outbid in both contracts, so I'm pretty comfortable in saying that was the primary reason.