Thin stainless tube is always hard, anneal it should help, but can you just switch to mild steel, or a chrome moly tube? 316 is a bitch when it comes to work hardening, it happens fast and is a seriously common problem. Boat tanks made out of stainless frequently fatique crack do to the liquid sloshing, alu or steel holds up far far better in thoes applications, like your magnitudes better.
Other option may be ditch metal, use a composite, they can resist fatigue loads far far better.
Work hardening is probably (bit) different issue. Stainless steel (or aluminium) is prone to fail at some point even if you don't stress it nowhere near yield limit if you just put enough load cycles at it. At 20khz you get 1 million load cycles in just 50 hours!
Most non-austenitic steel grades have nearly infinite load cycle life IF you manage stay below some certain stress level. IE:
https://www.mw-ind.com/pdfs/GoodmanFatigueLifeEstimates.pdf