How long should a boarding pass be preserved, after the trip? Is there any FAA mandate on the same to make any claims later?
If you have arrived approximately in time, picked-up your undamaged luggage, passed immigration and customs and doesn't want to use an airtrain (or something similiar) you should be able to safely discard it.  

Personally I tend to keep them as holiday memory, so I miss the old style tickets/boarding-passes from the 90ies :)