Example of ATS:
Unit 00's pilot has a SR of 53. He takes a full action on his first turn to fully spread his A.T. Field, giving him 5 ATS. On his next turn, he uses Neutralize on Sachiel, spending 5 ATP and thus decreasing his ATS by 5, leaving him with 0, but his field still spread. On the beginning of his third turn, his spent ATP, and thus ATS, refreshes to full and he may immediately choose whether or not to maintain the Neutralize power and for how much as a free action. For his next turn, he decides to only maintain it for 3, freeing up 2 ATS which he uses for other AT Powers. The turn following that, he maintains Neutralize for 5, again going to 0 ATS. When the battle ends, he stops maintaining neutralize, regaining all 5 ATS. If another target appeared, he would need to start up neutralize again, since he has stopped paying at least 1 ATP to maintain it.
Does that help, or do you need further clarification on some other part of it?