Spike and time out errors every x th minute
This is to help others as this was a very tricky solution to find:

We found below to be the problem where all the available core schedulers were not visible online

i.e we had SQL server enterprise edition because of which all 128 cores were not used and instead visible online were 40 only.

After upgrading to enterprise: core license , we were able to use all schedulers and viola!

Hope this helps as sometimes licensing could be tricky and we might skip