How many REST calls can I make at any given time?

I'm trying to write code to feed an internal monitoring tool we have here and so I've written code to spin up a Task (C# / .Net 4.5) for each of our, say 900-1200 monitored nodes/devices and query the Events table for each device. The problem I'm seeing so far is that many of the tasks are throwing A Task was cancelled exceptions and/or that the Task(s) have timed out after I .Wait() for them for FOUR minutes.

So, can anyone tell me what the limit of concurrent connections are to the REST [/Query] API?

Thanks,

Scott