Im programming an ATMEGA328P trough SPI and the only solution i cloud find was to burn the bootloader again every time i want to program it.
What settings are you using for your fuses?
I bootload my 328P chips as an Uno using the settings in the IDE (1.8.9 most recently) and I don't have that issue.
My designs use 16 MHz crystal, two 22pF caps, 10K pullup resistor on reset, and 0.1uC caps on VCC and AVCC (and also the 2nd Vcc pin for SMD parts).