Yes Broly can keep the power he gains after his fights because these are the results of his ridiculously powerful Zenkai boosts and his abnormally high potential. However, Goku theoretically has already surpassed Broly.

In the last arc, Granolah wished to be the strongest in the Universe, which was granted to him through the Cerelean Dragonballs.

Later on in the arc Gas uses the Cerealean Dragonballs to do the same.

Goku was then able to trade blows with Gas even if he was technically stronger.

This is because Goku now uses True Ultra Instinct (TUI), which is essentially Ultra Instinct Sign but amplified with his saiyan traits. This turns out stronger and more efficient for Goku since he cannot utilize PUI/MUI properly simply because he cannot stay as calm as the angels in any situation.

Now we see Broly training on Beerus’ planet in DBS Super Hero. However judging by this we can see that he can now snap out of the early stages of Ikari at will. Based on Goku’s reactions with him he still couldn’t fully control the form yet, and that’s a shame. Regardless of how strong he can become, he will eventually get knocked down as long as he doesn’t have full control of his power.

Kale, on the other hand, mastered her form rather quickly. It was previously unexplained but now I have a theory as to why.

Let’s go back to Broly’s Ikari form, which for now is shown to be unique to him.

We see in the DBS Broly movie that when beaten within an inch of his life, Broly’s sanity returns. He has dark lines under his eyes and yellow irises, indicative that he is using Ikari in conjunction with the LSSJ form.

Kale in her LSSJ2 form has the normal blue eyes of an SSJ. So my theory is to gain control, Kale doesn’t activate Ikari, uses LSSJ, and then ascends into LSSJ2 from there. Why does this matter?

I’m theorizing that it’s actually the Ikari form which is causing the loss of sanity. The LSSJ form by itself can be used with the user’s wits intact. However, I’m thinking there is a tradeoff in power here.

Kale is suddenly struggling against SSJ Goku when she fared better against him in SSJB form when she was berserk.

Meaning Broly SHOULD master his LSSJ form while using it on top of Ikari or else there will be a significant drop in power.

It makes sense because Broly’s Ikari SSJ is basically Golden Great Ape made canon and in human form.

That isn’t enough to even the odds with current TUI Goku though. To at least be on par with him, Broly must have an Ikari LSSJ2 form. Then he must unlock his potential. After that he should receive Spirit Control training in Yardrat, specifically mastering Healing. Then finally he should spar a lot with Jiren, so he can grasp the concept of the Relaxed state he always uses.

But if you would really like for Broly to surpass even Black Frieza, he should go back to his Yardrat training…

…and produce a Healing Factor. Imagine training and sparring so hard that even Broly would be at the brink of death, and then heal and recover at an alarming rate? He would effectively take advantage of his monstrous Zenkai boosts. It would also make him extremely hard to take down.

So in conclusion, though Broly can exponentially grow in power and keep that power after the battle, it’s not enough to be the strongest. TUI Goku soundly defeats current Broly, and he’s gonna need to go through a lot to even catch up and surpass him.