Does cron job remain in effect after computer reboots?

I have set up cron jobs using the following command

crontab -e

It seems that if a cron job is scheduled to run within the same day (i.e. computer has not been rebooted), then the cron job runs OK. However, if a cron job is scheduled to run several days later (i.e. computer has been rebooted at least once), then the cron job would be missed.

Moreover, every time when I use "crontab -e" to edit the crontab file in the "nano" editor, the top line shows that I am editing a different file, e.g.

File : /tmp/crontab.PLwi9Z/crontabFile : /tmp/crontab.degfpN/crontabFile : /tmp/crontab.odqbkT/crontab

I want to know that is this normal for crontab and how to schedule a job to run several days later (i.e. after several reboots). I am using an Ubuntu 12.04 amd64 system.

Thanks for any suggestion.