Purlins may sag because
they are overspanned
they are undersized
they are seeing more load than was intended
they were installed on their side
A 2 by 6 purlin should be installed so that the rafters rest on the 2 inch surface of the purlin, not the 6 inch surface. Purlins laid flat to the underside of the rafters are less effective. If you think of floor joists (the purlin is like a floor joist) it's easy to see how the purlin is strong when the load presses against the edge but is weak when the load presses against the flat side. Think of a purlin as a yardstick. Which way is it easier to bend? Again, the sagging purlins will show up as sagging rafters from the outside. Make sure you look both inside and out if you suspect sagging purlins. When in the attic, look to see whether the rafters are sagging. If the sag is not there, but in the purlins (where the purlin spans from one post or strut to the next), the pattern will be different, although you may not pick it up from the outside. Sight along the purlins as well as sighting along the rafters. This should tell you which are sagging.