Easy: he wasn't!
When Amy and Rory are finally married, time has been Rewritten by Amy remembering it all back. Rory apparently remembers a time when he was plastic, but he no longer IS plastic, because she remembered him back into existence as a human. At least, we can assume this is is the case, since he was able to knock up Amy, but has mentioned remembering all the times he's died/almost died/been plastic. My assumption is that to Amy, there was no difference between Plastic Rory and Real Rory since Plastic Rory had Real Rory's memories... So when she remembered him back into existence, she remembered a non-plastic Rory with all of the plastic Rory's memories. Which is weird, but not terribly implausible by Doctor Who standards. ;)
Any case, we also know (well, are led to believe, anyway) that Rory and Amy did, ahem, "it" (thus knocking up Amy) on their wedding night, which was spent on the TARDIS. Which does not contradict my working theory that Rory, while remembering something of his plastic days, is no longer actually plastic, as their wedding night occurred AFTER Amy Pond remembered everything and everyone back into existence. :)
It's very Timey-Wimey Ball and all that, but it makes a weird internal sense.
Side Note: It is entirely possible that when the Doctor "rebooted" the universe at the end of "The Big Bang" and sealed the time cracks that history was re-written back to the way it was always supposed to be (including Amy's parents existing and none of the planets that "fell silent" across the universe and forced their inhabitants away actually happened, which would not have started the whole Pandorica project started by the enemy alliance to protect the universe from the stars going out, ergo, no Pandorica, no "Cold Blood", no Rory dying and no need to be reborn as plastic) and that Amy and Rory remembering their experiences with the Doctor was as a result of their being TARDIS travelers and Amy having been at the center of the cracks when they first began in Series 5.
Response: A fair point, but it still begs the question of how Rory could "remember" being plastic, seeing as the consciousness in the plastic Rory was only there as part of a trap for Amy and the Doctor, having been taken, not from the unwritten Rory's brain, but from Amy's own memory... Unless you believe this was an early hint at her being able to remember things more accurately into existence due to sleeping next to the crack every night (which would be a fair point, since plastic!Rory fought against hist Auton programming, though a counterpoint to this might be "on the other hand, Amy's memory of Rory was him being devoted to her, so it's possible that emotion was artificially generated as well"). Either way, I think we're left at least partially with "Amy's brain being warped from the crack is partly responsible for Rory being human but remembering being plastic", as he was still apparently rewritten back into existence at the end of "The Big Bang", or at least rewritten back to being human. I think we can at least agree on that much, since he had to have been human by then to have knocked up Amy! ;)
Responce 2: Doctor has said that being a time traveler causes you to see the world and the universe differently and has said that with the crack in Amy's wall and all the stuff happening on the other side of the crack pouring into her head as she slept has "warped" her brain. The Doctor has said she was a very special girl and could remember things back into existence. Rory was remembered by her but he did have help by the Nestine scanning her room and learning about him, Roman soliders and Pandora's box before he was erased from history. And then after the universe was rebooted and Amy remembered the Doctor she was able to remember all past adventures. Its very much like in the Christmas Carol where Kazran said he could remember both versions of his childhood (his original and the one the Doctor changed) at the same time. Several adventures where history completely changes the characters can remember both version's of history (Panorica/Bang, Last of the Timelords) due to their closeness to the event (eye of the storm). Rory in this case was rebooted into existence as a human and when the Doctor was remembered back into existence all memories of previous adventures were too.