When I try to resume a download from specific site, IDM wants to download a file from the beginning. Why is it happening? How can I solve it?

Maybe this site uses temporary links and refreshing link address for this download will let you to continue downloading the file.

If it does not help, then it is impossible to resume a download from this site. You will have to redownload it from the beginning. If you have often network problems or this site is not stable, you may try to leave this file alone in the queue and press "Start Queue" toolbar button in IDM main dialog. IDM will keep trying to redownload this file until it is completed.