No, not having enough free space does not cause a delayed write failure.

Check the S.M.A.R.T. status of your drive using a program such as HDtune, just in case it's on its way out. You should also schedule a complete chkdsk:
Start > Run > chkdsk F: /R /F
And then answer Y when it asks if you would like to schedule the check on the next boot. Then reboot.