"clung to the hope of ---"

"clinging on to (the) hope"

"clinging onto the hope of winning" 

"they clung on to the hope of winning" 

"clinging  on to win"

"to win they have to cling on for one more minute" 

"they have to cling on for one more minute to win"

"they must cling on" 

"they must cling on to win"

"I always clung to that hope he would pull through, that he would be in a coma and his brain would recover, but we were past that stage." From the second boxing article 

"I always clung to the hope (that) he would pull through" = correct natural way to say it. That = optional

"I always clung to that hope he would pull through, ---" = he clung to the hope, that hope is implying that hope we would all have for somebody to pull through. The writer has not gotten the boxers quote across very well 

"I always clung to 'that' hope he would pull through,--" putting that inside it's own quotes makes it clearer to my thinking and style of writing. 

As the South Africans clung to the hope that a breakthrough would accompany the new ball, North and Haddin picked up their half-centuries in comfort.

From the first article "clung to the hope" = perfect (clung to the hope that +( ---- ) 

you wrote "clung to the hope to win" = wrong "clung to the hope of winning" = correct

I would write it as: 

The team clung to the hope that they could win and scored in the final minute.

To me, cling to hope sounds like more of a poetic, written phrase.