There are no Microchip (or Atmel, Freescale, Infineon, Renesas, ST, TI, etc.) offerings that have non-volatile Static RAM. The only MCU's with non-volatile RAM are a few from Fujitsu and Ramtron - however, their RAM is implemented as FRAM (ferro-magnetic RAM) which is quite a different technology altogether.

There are also external RAM devices based on the above mentioned FRAM and BBSRAM (battery backed Static RAM) from several sources.