There's no limit to how many times it can be frightened. Several builds would still allow you to do one or more attacks in addition to . The target may or may not be able to leave combat, but if they waste their turn leaving nothing stops the PC from repeating next round.
This is would be a particularly useful tactic if the target is the commander of a bunch of lower-level support type folks.
Umm, so, why aren't the bunch of lower level mooks mobbing our intimidating hero, forcing him away from the commander so, that he cannot intimidate him next round? Remember, you have to be within 30 feet. Should be a pretty simple thing for the mob to block the PC while the NPC moves away (most humanoids DO have at least 30 feet of movement).
And, why does our commander NPC not have proficiency in Insight? Seems like a pretty common thing to have for leaders. Looking over some of the humanoid NPC's in the MM, we see the Cult Fanatic and the Knight both have advantage on fear saves (which I'd argue should apply), and our NPC Noble is trained in Insight.
Now, at the point where you're talking about this becoming an auto-success (because, remember, we're only talking a +2-5 on a skill check), we cannot really use ANY of the MM humanoids straight out of the book. Certainly not for any of the leaders. They just don't have enough CR to make an interesting encounter.
.... hang on a tick. How exactly are we getting intimidate scores that high? Even with a 20 Charisma, you're only talking about a +15 on the check with this feat at the absolute maximum. What else bumps Intimidate checks? It's not like perception where you can stack a bunch of other stuff on there.
So, using a standard array human, we're talking MINIMUM 8th level fighter or 10th level rogue or 12th level anything else to do this. 2ASI's in Cha and this feat. And, at that point, they're still only +11-13 on the check. Which is not an auto success. Unless they take 11 levels of Rogue to get Reliable Talent. At which point they are giving up sneak attacks (they only get one attack) to potentially frighten a single humanoid NPC 1/round.
And you think this is broken? Seriously?