You are miss remebering the first fight
https://www.youtube.com/watch?v=VOdkIo2Cark
Bucky was screwed until the copter started shooting T'challa. That is when he started taking off, he turned to fight when T'challa first tackled him
Then t'challa chased him down and was about to kill him again until steve tackled him in the tunnel thing
Second fight was a draw but "not pressing his advantage" is a little much considering landed on all fours after getting hit.
And he didn't stop trying int he third fight, they had each other by the throat. Bucky had the advantage (two whollops), grabbed by throat, then the "why did you run" lines, then tchalla overpowers him, gets his licks in, then was about to killl him before being tossed
https://youtu.be/Vwgygi3niVI?t=309