According to the HP Quickspecs (http://www8.hp.com/h20195/v2/getpdf.aspx/c04123266.pdf?ver=1) this server model contains the NC553i, which is an OEM branded Emulex adapter. As shown in the ESXi 5.x Patch Matrix the "elxnet" driver was replaced with the builds you mentioned, which may be related to your issue. According to the HCL for the NC553i adapter, the required driver can be found at https://my.vmware.com/web/vmware/details?downloadGroup=DT-ESXI55-EMULEX-ELXNET-1051217&productId=353 respectively https://my.vmware.com/web/vmware/details?downloadGroup=DT-ESXI60-EMULEX-ELXNET-1051217&productId=491. Alternatively you can download the same driver from HP's support site (http://h20565.www2.hpe.com/portal/site/hps -> "HPE Servers, Storage and Networking"). The recommended firmware version for the adapter is 10.5.96.0 which is included in the latest SPP (HP® Servers - Service Pack for ProLiant).
Once you are on ESXi 5.5 Update 3, or ESXi 6.0 Update 1, consider to update "esx-base" to the latest (for details see https://esxi-patches.v-front.de/ESXi-5.5.0.html)
André