Hmm, maybe oxidation? Do you take care not to splash the wort around when it's hot, or after fermentation? Also, what are the conditions your keeping the bottles in? Are you leaving as little head space as possible when bottling?
This may be a stupid question, but how about pouring? Do you leave the last bit or pour the whole bottle in? I wouldn't think that would add a cardboard flavour, but it would add sweetness at the end (the yeast).
I typically swirl the wort chiller around when cooling down the beer. I use an autosiphon and bottle via the normal approach. It foams up a little when bottling, but I use oxy caps to get rid of that last little bit of oxygen.
I leave the last bit out, typically.