Great explanation from @janbb.
I would add that the expression should be taken in two parts. It’s not a unitary phrase. “At times” just means “sometimes” or “occasionally” or “now and then”: in other words, interrupted and not constant, with instances lasting for short periods relative to the whole duration.
The frequency relates to how long the total period of time is. In the case of the debate, “at times” implies intervals of minutes, because the whole thing was less than two hours long. But if we were talking about, say, a forty-year career, things that happened “at times” might occur years apart. You might read, for instance, that a movie actor with a lifetime of starring roles had at times given performances that were best forgotten.
“Reduced” suggests a hierarchy of possible actions, with the ones at the top most preferred and the ones at the bottom least desirable. It means having moved down that hierarchy. A person in reduced circumstances is less well off—that is, poorer—than before.
Being “reduced to” something means being brought down to it by some adverse situation. The person is diminished or made smaller in some way by having to choose a lower option. It’s never a good thing. You might say, for instance, that a person who had lost his job was reduced to asking for handouts from his parents, or that someone who’d lost an argument was reduced to calling her opponent insulting names.
In the quotation you cited, Mr. Wallace is brought down or diminished by the position he’s in and must stoop to begging Mr. Trump to stop speaking. There’s a suggestion of helplessness or desperation. By the time he has to plead for compliance, he has already lost control of the situation.