I carry it around everywhere I go actually. Just because I have the phobia that immigration may stop me at any point. I haven't lost it yet but I completely understand what you mean. A quick tip if it helps, as soon as you receive your EAD, do an appt for your license. And if you have a stable job and they already have your info yo won't need your EAD. The issue is that everytime you renew it I believe they must take a copy of your last EAD, or at least that's what I have had to show. Good luck.