No, you won't have to purchase it again.
This is from the itch.io support:
After the purchase
The download page is the first thing the buyer sees after buying a game. Here is what it looks like:
At the top of the page is a detailed description of the transaction and any important information regarding how the download page works.
It reads:
This page has a unique URL for your purchase. You can always re-download the latest files from this page. You should have also received an email with a link to this page. If you ever lose the URL for this page you can request it to be emailed to you from the support page.