Generally speaking, over the course of a story or campaign you are trying to help build up the characters. Now by 'build up' I don't necessarily mean turn them into omnipotent god like creatures, but rather that the characters show growth over the course of the story. It is partially what gets people emotionally invested in a character, they watch them grow as the story goes on, as hardships are experienced and dealt with the character grows and changes. Weaknesses may show, but so will strengths. As the hardships and obstacles continue, the character will grow stronger in some way or ways, and this growth will usually reflect on the theme of the story.
For an example, many battle anime and manga have the theme that hard work and sacrifice are what lead to true strength, not birth right. As such, the main character is usually some common person who is presented as having no talent what so ever. However, over the course of the story through hard work, suffering, and sacrifice they become stronger, over coming their obstacles and moving along. Because this strength is gained through hard work, they will often acquire followers and friends, and even enemies will come to admire them. Often, this method of hard work has been in place for a long time, giving the character a massive amount of stamina and making their usual way of winning being to get beaten on, persevere, and eventually win through a tenacity that can only be gained from the hardwork and sacrifice that they have done. While it is not often said, I think Naruto coined the term properly when it called its titular character a "Genius of Hard Work". Essentially, someone who is good at working hard and thus (while not said, implied) gets greater gains from it because they always do it.
However, building up characters can lead to issues, especially over time. So you have your character who wins this way, it's not pretty but they do win this way. Only, the audience, the player, or you want more from the character. They've been working hard, putting in their time, it is time to show that they have grown. So you show it, you show how much they've grown and the next obstacles aren't ones that are set up to be maximum challenge for the person, but ones to show that they have grown. So you build up these new threats a bit, to show that they are serious obstacles, but then let the character surpass them easier than normal. It shows strength, it shows growth, it really is a good thing to do because it shows that those past triumphs are not meaningless, the person is growing from them.
Of course, now what happens when you want to go back to the old way for whatever reason? Yes, the character has grown and you've shown that, but you also want to focus again on their tenacity, their never say die attitude? So you ramp up the next challenge, and you make it harder than what they've been facing. After all, those were designed to show how much the character has grown, how much stronger the character has become. This is designed to show that despite the growth, the character is still as tenacious. In short, this is designed to bypass the growth to show the foundation. The only problem is, bypassing growth makes the audience feel cheated. By bypassing the growth, you essentially appear to be stripping it away from the character. Sorry about that, that growth didn't actually happen, they still rely on this one core aspect. Not a good show at all.
So what do you do? Can you even still do it? Yes actually you can, but it takes more work than it used to. You've shown the growth, you've shown the build up, and so now to bypass it you need to work harder. You need to establish the threat as a threat a lot more, build it up and build it up well. Also, you shouldn't just bypass the character's growth, instead you should address it. Show the growth, if it is a fight make it go back and forth as the character's growth helps them through the fight, but the other person is still just that bit better. Acknowledging the growth helps with cementing the build up, you didn't just removed it. It is there, it is just that this opponent is stronger. What the character is trying is working, just not enough for the win to come to them. Not yet, not right now at the very least.
Also, unless you are very clearly talking about vastly different levels of power, or are deliberately trying to annoy the people in your audience (be they players or otherwise), do not have this new obstacle just completely dominate without any reprieve up until the moment they lose. This goes with acknowledging the growth that has happened, but any time someone an audience has grown with is simply "toyed with" it isn't acknowledging the growth, it is ripping it away.
Essentially, once you've given growth, and shown growth, you shouldn't take it away. At the very least you shouldn't take it away without some very good story reason for it.
Also, while this has mostly been focusing on the issue as a narrative thing, you need to keep it in mind as a GM as well. If Players have gotten used to feeling strong, even when challenged, they are likely to feel betrayed when suddenly something stomps all over them. The feeling of being powerless is even more frustrating when playing a character, because it is you who are powerless, you are not reading about someone else's character, or something where you have no control. You have control, supposedly, you just can't do anything. It starts to feel like railroading, and it can seriously damage the mood or atmosphere around a game. The build up to a threat like this in an RPG is even more important than in a story, because the players need to understand what it is they are getting into when they jump into the ring with that monster. If they don't know going in that they are going up against something that is more than just the monster of the week, it can turn out very bad when they just get rushed. It can also feel even worse if they then get a "lucky shot" that turns everything around for them. It feels forced, and it grates on most people. At the least, it grates on most people I've talked to about this.
So remember, if you are switching from showing growth to encouraging further growth or showing the core foundation for the growth, you need to work it a bit harder, work the build up better and make it memorable. Most importantly, keep it fun, and being tooled on is not fun.