my friend and workmate Pascal Di Marco ran into some VMware connection limitation while backing up 4000VMs in a very short backup window.
If you ran a lot of parallel backup jobs that use the VMware VADP backup API you can run into 2 connection limitations… on vCenter SOAP connections and on some limitation on NFC buffer size on ESXi side.
All backup vendors that use VMware VADP implement in their product the VMware VDDK kit which help the backup vendor with some standard API calls and it also helps to read and write data. So all backup vendors have to deal with the VDDK own vCenter and ESXi connection count in addition to their own connections. VDDK connections vary from VDDK version to version.
So if you try to backup thousands of VMs in a very short time frames you can hit these limitations.
In case you hit that limitation, you can increase the vCenter SOAP connection limitation from 500 to 1000 by this VMware KB 2004663 http://kb.vmware.com/kb/2004663
EDIT: In vCenter Server 6.0, vpxd.cfg file is located at C:\ProgramData\VMware\vCenterServer\cfg\vmware-vpx
As well you can optimze the ESXI Network (NBD) performance by increasing the NFC buffer size from 16384 to 32768 MB and optimize the Cache Flush interval from 30s to 20s by VMware KB 2052302 http://kb.vmware.com/kb/2052302