Generally speaking IF wire-braid is failing due to vibration resonance, then its a mass/mechanical interaction. Changing wire braid materials... except for increased stiffness and/or mass... probably won't produce effective results.
A MINOR reduction in wear/damage rate might result if copper wires have nickel [Ni] or tin [Sn] or silver [Ag] coating which will change friction by improving fiber-to-fiber lubricity.
Example of a wire system that needs special coatings for improved long-term fatigue-wear protection, is thus...
High strength carbon steel 'aircraft quality flight control cable' [MIL-DTL-83240] has strain hardened carbon steel filament wires that have a zinc coating or tin-over-zinc coating applied. The zinc [on the steel] is for basic corrosion resistance; the premium control cable [usually specified 'just because it much better'] has tin-coating applied over the zinc-coating for improved lubricity... and which also seals the zinc coating for better corrosion resistance. When each steel fiber is coated this way, the fatigue durability of the wire rope is substantially better than just zinc-coated wire-rope [any helical twisted 'construction'].
Although this wire rope example is substantially different than copper wire braid, the 'similarity of example' may hold-up, even though electrical grade fine copper wires are far more damage prone that steel wires. OBVIOUSLY, ONLY testing would be able to evaluate whether any of these coatings will provide relief from Your problem.
NOTE.
Braided copper electrical shielding wire spec that I've worked with for 'special shielding' problems is as follows...
A-A-59569 BRAID, WIRE (COPPER, TIN-COATED, SILVER-COATED, OR NICKEL COATED, TUBULAR OR FLAT). [Replaces obsolete QQ-B-575]
Regards, Wil Taylor
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