The script is very simple read of a database and output to HTML,
It is possibly a cumulative time they are looking at rather than the script continuing to run, Perl scripts, like Python and PHP (other scripting languages are available) end when the last instruction is processed.
Assuming this is a process that runs on a HTTP server and executes on a URI request, it will always run as the account/site 'owner' so for the rather simplistic process monitoring will appear to be the same process instance continuing to run rather than every new instance of the script running and ending.
I see this same thing on our 'shared' servers with spamd/spamassassin processes running as the account user name. if the server hasn't been restarted for any reason, these processes might seem to have been running for several days, but they only 'wake up' when an email message is processed, which only takes a few milliseconds but many thousands of individual message scans clocks up several hours worth over a couple of months.
So I would suspect that your hosting provider 'technical' support are not too clued up on process monitoring and are treating 'top' time stats as continuous 'running' time rather than it being a cumulative time since the last server restart.
And as it is a 'shared' environment ... it's probably NOT even your site or scripts that are causing the slow load times.
Chris.
Indifference will be the downfall of mankind, but who cares?
Time flies like an arrow, however, fruit flies like a banana.
Never mind this jesus character,
stars had to die for me to live.