If I understand correctly, dust particles with a size of 0.1 microns are estimated to survive against sputtering or collisions with other grains for ~ 10^8 years. This suggests the spacecraft could survive trillions of years before substantial erosion, or more if the rate of supernovas in the galaxy declines with age.

A competing process over the very long term is repeated close encounters with stars and stellar remnants. This tends to add kinetic energy to lighter objects. So, one would expect the spacecraft to gradually acquire more kinetic energy by random close encounters and eventually be ejected from the galaxy.