Why could they not make more rings?
 

Is there a reason why the Elves couldn't create more magic rings than the Three? What is so special about those rings?

Howdy Metro...
To my understanding, the makers of the rings of power(especially Celebrimbor, the main creator) were very special and talented. Celebrimbor was killed by Sauron so my answer is that there was nobody around with the skill to make more rings. Sauron's ring still existed and elven smiths didn't have the talent.

Perhaps also once they relized that Sauron was trying to control them through the rings, they didn't want any more. For Sauron's ring, it drained a lot of his power, the elven rings probebly drained the Celebrimbor's power to some extend as well. He could probebly only make so many rings before there wasn't anything left for him to use.

Most of the Rings actually lost some of their power as Sauron took control of them. Their fate was linked to that of the One Ring, so any other Elven ring that was made would have fallen under this spell, and had no power. Also, the makings of any other ring of power would have alerted Sauron when he was in control of the One, as he had control of the Nine and most of the Seven already. This would probably lead to him discovering the Three, and ultimately take over the world.

i think that they thought that the one ring could take control of their rings so they didnt make any new rings

or

they didnt have the art or skill of making those rings. i think only the elder elves had that skill

If they had enough power,they could have created more rings,and Sauron couldn't corrupt them (or that's what I think),but the best creator of the rings,Celebrimor,was killed,and the knowledge of forging the Great Rings was gone.It says that Three were made by Celebrimor himself without anyone else.So,when Sauron killed him the knowledge was gone.Sauron maybe had some knowledge about it,but not enough to forge new Rings and the Noldo wich helped Celebrimor most likely sailed to Valinor.