Which version of Veeam software for the backups? Also any reason to run the ESXi 5.1 version?
First, Cant predict without the logs.
First,Check if your vnic and HBA drivers are updated. However from VMware prospective ESXi 5.1 is out of support from September 2018.
5.1 has stopped being supported since August of 2016.
In order to give OP any assistance, we need more information including specific PSOD information and exact build of ESXi. It would also be helpful to know details on the hardware on which you're running ESXi. Asking along with Sateesh, any reason why you're still running such an old version?