While reviewing a design (not mine) I came upon a situation where repetitive pulses exceed reverse Vbe so much that it'll cause breakdown. It's only around a milliamp at 10-20% duty cycle but this can go on for weeks, months, years. Some studies show a steady deterioration of beta but they are looking at much higher reverse base currents such as 60mA here:
A slight deterioration which then reliably plateaus would be ok while a steady slow drop in beta would be problematic. How about 1mA with a regular run-of the-mills 2N3904 type?