The first stages of planet formation take place in protoplanetary disks that are largely made up of gas. Understanding how the gas affects planetesimals in the protoplanetary disk is therefore essential. In this paper, we discuss whether or not gas flow can erode planetesimals. We estimated how much shear stress is exerted onto the planetesimal surface by the gas as a function of disk and planetesimal properties. To determine whether erosion can take place, we compared this with previous measurements of the critical stress that a pebble-pile planetesimal can withstand before erosion begins. If erosion took place, we estimated the erosion time of the affected planetesimals. We also illustrated our estimates with two-dimensional numerical simulations of flows around planetesimals using the lattice Boltzmann method. We find that the wall shear stress can overcome the critical stress of planetesimals in an eccentric orbit within the innermost regions of the disk. The high eccentricities needed to reach erosive stresses could be the result of shepherding by migrating planets. We also find that if a planetesimal erodes, it does so on short timescales. For planetesimals residing outside of 1 au, we find that they are mainly safe from erosion, even in the case of highly eccentric orbits.