I'm now lawyer, but I just recently purchased a new home, the contract stated that the builder covered everything under a full warranty for one year. Beyond that, all maintenance, upkeep, repairs, etc are up to the buyer. But even if it is in the contract, I believe it is still possible to sue, if you can prove negligence.
Even if you had a home inspection, the scope of the inspection would rarely discover faulty materials, unless it is something blatant that is visible to the naked eye, and usually the warranty on home inspections, at least in my limited experience, was only a year also.
You may be up a creek, but I would definitely talk to some of your neighbors who are having the same problems, get their opinions on the subject, talk to a lawyer, and maybe get someone with some expert advice on the trim that you are having a problem with. See if this is something somewhat common that he/she has heard of before, or if there was some definite negligence on behalf of the builder.
Good luck.