In short, any mechanical finishing (blasting, abrading, cutting, milling, turning) that removes even a very small amount of material from the surface of the substrate will remove the passive layer given from passivation processes on stainless. This also applies for welding; welding material will not necessarily form a passive layer naturally and any free iron present will begin to corrode and spread at an ever-increasing rate. If significant scale is produced by a welding process the part may require pickling prior to passivation.
Passivating stainless steel is a way to prevent it from rusting/corroding. In many people’s minds stainless steel is a magic material that doesn’t corrode. This is false - some grades of stainless steel are much less corrosion resistant than others and others, even 316 stainless steel (A4 stainless) can corrode - especially in the presence of contamination.
Passivation must be done after all mechanical, welding or other high temperature operations have taken place. The passivation process can be safely repeated if a part is modified. Ideally passivation should be the last step before assembly of the finished product or the application of any coating (e.g. painting, selective electroplating). Selective passivation or post-assembly passivation should be avoided due to the many chemical/material compatibility issues that can arise.
While it's important to avoid deliberately or accidentally removing the passive surface layer, the benefit of using stainless steel for a part is its natural resistance to corrosion. Passivation is a way to improve that further and reduce variability due to its prior condition. This is why some consider it to be a cleaning treatment, rather than protective treatment in itself. Compared to other protective treatments on less corrosion resistant base materials, the consequences of a scratch is rarely serious in most applications due to the natural corrosion resistance and depending on composition and chemical environment, self-passivation can occur providing some degree of self-healing. Nonetheless, this is not an excuse for not following careful assembly practices and it's still extremely important to avoid contamination.