Hi there,
Liz has already replied to your question, I would like to add some info, hope this may help.
You write, that:

it...causes the error if there's no activity for 8 hours.

perl.apache.org describes the so called morning bug suggesting setting the wait_timeout mysqld system variable during the mysqld start to a higher value.
I know, you said, you can't make any changes to mySQL (MySQL?), but the same document also sends to the Apache::DBI documentation. I am not getting into details, because there is no point in retypeing what has been written in there, but what applies to your problem:
It describes:

1. The ping() method and its example.
   
2. The way to configure the usage of the ping method (Apache::DBI->setPingTimeOut($data_source, $timeout)).
   

Practical mod_perl book says, that this issue applies to old versions of DBI/DBD. As you don't provide any information abut versions the server is using, I can't suggest upgrading.
Also on PM site dug in 306648 thread and pope in 185416 node write about the "morning bug".

-sheep