302 Redirect with cron.php

Question

On a rather old drupal site (D5) I get a 302 on calling cron.php when doing this via wget or curl. It worked fine for many years (via crontab). If I use a browser for that I get a 200 and a blank page (which is normal) the cron runner runs successfully. After trying to find a solution for a couple of hours it works fine with curl for no apparent reason, but not with wget and only if I run it directly (still 302 with crontab). As I type this I try again just to make sure and now neither wget nor curl work anymore, but running it through the browser still works just fine. Strange.

curl: curl -s http://www.mysite.com/cron.php
wget: wget -O - -q -t 1 http://www.mysite.com/cron.php

Any ideas?