There's a clear indication that MindFlayer Billy did something deliberately to El/Elle/Eleven. From S3E7: The Bite (transcripts from here)
ELEVEN: He said he was building something. That it was all for me.
(snip)
LUCAS: So, he's building an army, just like we thought.
MIKE: Yeah, but he's not building this army to spread.
WILL: He's building it to stop Eleven.
MIKE: Last year, El closed the gate on him. I have a feeling that really pissed him off.
LUCAS: Like, royally.
MIKE: And the Mind Flayer now knows that she's the only thing that can stop him. But if she's out of the way --
LUCAS: Game over
When they confront the Mind Flayer, the Mind Flayer grabs Eleven's leg and leaves... something in her (the titular "Bite"). That takes us to S3E8: The Battle of Starcourt
EL is SCREAMING in pain. WILL, LUCAS, ROBIN, STEVE, MIKE, MAX, DUSTIN, ERICA, NANCY and JONATHAN are struggling to
help. El’s leg starts BUBBLING.
ERICA: What is that?
MIKE: There’s something in there.
Eleven has to basically pull that piece out
As everyone looks on, El begins to use her powers to draw the thing out of her leg. She struggles. Her nose begins to bleed. The thing comes closer and closer to the surface of El’s leg.
JUST THEN, El SCREAMS! The GLASS WINDOWS of THE GAP STORE SHATTER.
The thing is a CHUNK OF THE MIND FLAYER.
That's the last time we see her able to use her powers. Eleven tries to crush a can before the big fight with the Mind Flayer in Starcourt and it's clearly not working from there on out.
The problem with the "Eleven was tired" theory is we've seen her weakened before from being tired. She usually bounces back in short order (I mean, she closed the gate in S1, which was clearly taxing, and did not lose her powers).
The implication is the Mind Flayer's bite did something to Eleven (they named a whole episode after it, which calls attention to it). This is furthered by the fact that the Mind Flayer directly sees her as its greatest threat and goes to great lengths to neutralize that threat. They only beat the Mind Flayer when they destroy the Soviet portal to the Upside Down.
What about her powers returning slowly? It's probable the Mind Flayer only got part of what it wanted with her powers disabled temporarily so it could kill her. It's unlikely it had any plans beyond that.
