Many NPCs have been given keys to the strip gate as a way around this glitch. It should be addressed in the next patch or so but for now you can do a couple things to get around it:
-killing one of the gatekeapers while sneaking and from a long distance (sneak kill from long distance will not damage faction standings)
-bring up the command console, click on the gate (it should say door or gate in white letters up at the top of the screen. if not then move closer) and then type "unlock"
-use the console command "player.additem 00119875" to add the gatekey to your inventory.
The last solution is probably the best if you have met the requirements to get in but are simply locked out for no reason. To avoid it interfering with steam acheivements you should save the game after adding the key and exit and restart the game and then load the save. Steam acheivements are disabled for the session in which you use the console but not for an entire playthrough.