deleted purchase and can't repurchase

No, most of the time you do not have to "repurchase" depending on your country's regulations.

To recover an accidentally deleted purchased music, follow these steps:

1. Open iTunes on PC and log in
2. On the top bar, Account > View My Account...
3. Scroll down to iTunes in the iCloud and click "Manage"
4. Find the hidden purchased song and unhide it

To re-download a hidden purchased music, you have to restart the procedure and follow these steps:

1. Head over to (iTunes) Store
2. Click "Purchased" from MUSIC QUICK LINKS at the bottom right of the screen
3. Find the purchased song you want to re-download and click on its cloud icon

(Please note that the 2 procedures above is a one solution. You really have to access 2 different screens of Hidden Purchase, one just to unhide and another to recover.)

Ok so this happened to me too. I'd deleted an album intentionally because after 2 hours of trying everything to make it play it just wouldn't. When I tried to repurchase it I found that I couldn't.
What I did was click on the arrow to the right of where it said 'purchased' and selected "give as a gift" (or something similar) I then sent it to my own email address.
That worked.

Did you delete the file from the hard drive or the entry from the library? If there entry is still in the library then when you visit the Purchases section of the store iTunes won't show the track as available for download.

tt2

I once deleted a (cheap) song in my iTunes Library that I had purchased in iTunes from a Greatest Hits collection because I wanted to rebuy it from the original album (with the original artwork). However when I went to repurchase the song from the original album, iTunes would not let me purchase because it said it was already purchased. I looked in my PC's "recycle bin" and the song was there. Once I emptied the recycle bin I was able to purchase again.

Why can't you download them? Any errors?

What country are you in? Downloading of past purchases is not available in all countries.