Is oracle computer capable of doing infinite loops?
I'm with Yuval Filmus on this. Oracle seems to be the wrong characterization. An oracle is normally thought of as something that can decide a problem asymptotically faster than a Turing machine (or at all, for undecidable problems).

What you're describing sounds, perhaps, more like hypercomputation. Consider, for instance, a Zeno machine. It could output "True" after 1 minute, "False" after an additional 30 seconds, "True" 15 seconds later, and so on, completing the task you set out for it in two minutes.