I am just wondering if bystander tokens can keep getting KO'd, spawning the other bystander token back and forth for unlimited amount of times (or can only 1 bystander Batcycle, and 1 Batwing token be placed once per a game)?

I read it as 1 time based on the word "that" and how it works in English.

That being said, "that" isn't a game term so I can see the reason one would say it is unlimited.

Sure it is, all words are 'game terms', just some words have specific meanings beyond the English definition. In this case, 'that' would be referring to the bystander placed at the beginning of the game. So each vehicle can only be destroyed once.

Exactly. The game mechanic for placing these bystanders does not allow for for the KO'ed ones to be brought back into the game.

Here is how the E&C describes KO