The schematic has some serious flaws as I can see

1) As it stands, the switches can seriously damage the A & B segment outputs as the supply is directly connected to the port. If the segment is logic 0, it directly shorts the supply to the port pin which may blow the pin or simply short the supply (your reset issue lies here).

Way out?
1) The cathodes need series resistors of around 100 Ohms.
2) A 100n capacitor between VDD and VSS directly across the PIC
3) Lots of b/cheer ?