I imagine it's the remote DB server that's giving you the message. Either it has a low limit (set by your user license?), or you have a lot of scripts that are tying up connections. I know this doesn't quite answer your question, but in the absense of log information, look to the information you do have.

Additionally, I'd consult with your database vendor (Oracle? MS SQL server?) about client packages they offer that might have the monitoring features you're interested in. You don't tell us what type of environment you're running under so it's impossible to even guess at a Perl recommendation. You may be able to do this by parsing DBI trace data for all of your scripts, but this is going to be pretty complex and difficult to do in real-time.