Thunderbird alerts when expected email does not arrive

Thunderbird alerts when expected email does not arrive

I am on Ubuntu 12.04 using Thunderbird as email client. Both are up to
date in terms of updates.
I have bunch of nightly jobs that do the work and send a status mail. It
gets tedious if you keep getting same/similar mails every day so I ended
up writing a mail filter rule which causes emails to end up in their
respective folders automatically. If things are going ok, I really don't
need to read emails. Failure emails are sent to different alias - if the
job runs.
We recently discovered that one of the job had not run for few days as
someone accidentally disabled it. In order to avoid such problems in
future, I would like to setup thunderbird in such a way that if I don't
get email from given address within given duration, it should alert me. My
dream solution is to set up frequency - some jobs do run every 4 hours.
Is this possible? Can I setup Thunderbird (preferred) or other email
client for reminding me when expected email does not show up.