So, there is the possibility that he was advised by the police not to broadcast that he recorded it.

But, assuming that is not the case, then I think there is something suspicious about it. Before he called him the first time, he said that he thought "oh my god, should I get some recording software for my phone?” So it did occur to him to record it...

I get that, the first time, he was under pressure to call him within the 10 seconds. But, the second time, he had plenty of time to think it over, and had just heard 2+ minutes of ranting and threats to his life and his loved ones. He said that he was really scared, but doesn’t express much remorse or regret for not recording the calls (first one, a bit. Second one, none at all)? Wouldn't anyone of a reasonable nature, after a traumatic experience like that, feel shaken and regretful about not recording it... and be kicking themselves mentally & emotionally for not capturing this evidence, which is of a huge and personal nature?

He has created videos documenting the evidence of Pizzagate on Youtube, and so is not new to the Pizzagate investigation. I presume that he knew that people have died investigating Pizzagate, and knew the importance of gathering evidence. He stated this before the first call and yet, didn't think to record the second? Which also contained a death threat - “he assured me that I would die if I didn’t take this video down.”