Well, your dilemma really isn't a Perl problem:
When your data needs to be so absolutely current, you mustn't cache it.

Cacheing or using some other way than reading and computing lots of text files might reduce the stress on generating the data.

Improve hardware and the algorithm if you can and push towards migrating to a more viable solution.
Some kind of cache or a fast database, whatever might do the trick.

Cheers, Sören