I'm wondering if it might be a case of Spider Mites?
http://www.ext.colostate.edu/p...
There's an image here of what the webs look like:
http://en.wikipedia.org/wiki/S...
An image of the insects and damage :
http://files.growery.org/files...
Information at this link:
http://www.wikihow.com/Get-Rid... explains how to spot them and shows photo's of damage etc.
I've never had an issue with Spider Mites but I use a product called Safer Insecticidal Soap:
http://www.saferbrand.com/advi... for other houseplant pests and it's said to work for mites also. It's usually available at Home Depot and Lowes and works for aphids and mealy bugs.