Sorry to dig up an old thread, but Im having exactly the same issue here.
Im running Veeam 220.127.116.115 on WIndows Server 2012 R2.
Veeam throws the error "Unable to allocate processing resources. Error: No backup proxy is able to process this VM due to proxy processing mode restrictions." when backing up a couple of VMs which are part of a bigger job.
VMs are on the same LUN as other VMs which are backed up successfully within the same Veam Job, so its not access to the LUN or VM thats the issue.
This started last week when some VMs were migrated from one LUN to another. This hasnt affected all of the VMs that were moved however. This has affected only 2.
I have rebooted Veeam and confirmed nothing else is going on (proxy/storage) at the time of the jobs. The failure is a consistent one which happens every backup for the same 2 VMs.
Can anyone shed any light on previous solutions to this, other than the obligatory "reboot veeam"?