I bought a game off of itch once(Vintage Story), and the price increased at one point, but the download button was still accessible for me.
If it works anything like that does then it's likely you won't.
Unless there's a button for the game maker that makes people that already spent money on it have to pay again, but more likely if they do increase the price and you have to pay again, then it won't be the full price and you'd have to pay however much the additional money. (For example, this game costs $7.99 USD, but they upped the price to 9.99. If there IS a button that makes people pay again, then you'd probably only have to pay 2 dollars.)
I don't think they'd do that though, but take my words lightly as I don't know what I'm talking about fully lol.