<p>Is there a limit with the number of SSL connections?</p>

<p>We are trying to connect through SSL with 2000 sessions. We have tried it a couple of times but it always dies at 1062nd. Is there a limit?</p>

Yes, everything has a limit. As far as I'm aware, there is no inherit limit with "SSL".. it is after all just a protocol.
But, there is a limited amount of memory, ports, CPU on the machine you are connected to, from and every single one in between.
The actually server you are connected to may have an arbitrary limit set too.
This question doesn't have enough information to answer beyond "YES".