Personally, I am of the opinion that those records should be kept electronically and in perpetuity, if not by the TPA/RK/Trustee/Custodian then certainly by the plan sponsor with the assistance from one of the aforementioned entities. Doesn't need to be extensive, just needs to sufficiently prove someone has been paid out.
Why?
SSA sends me a letter saying my employer's plan from 35 years ago MAY owe me a benefit. Not remembering they paid me back then and instead of rolling it over I went to the casino and lost it, I have no record, so I make a claim on that plan. I don't accept their answer of we don't have you in our records any more so you must have been paid out, so I go screaming "I want my two dollars!" (bonus points for the movie reference) and threaten to talk to my lawyer, the DOL, the IRS because I've seen everything worthwhile on Netflix and have nothing better to do now. This sends the Plan Administrator scrambling, calling around to past and present service advisors, muttering "I don't have time for this" and "I'm getting too old for this sh1t" (yes, another movie reference) before caving like a Democratic senator and concluding it's easier to pay me my $2.
The moral here is (1) someone should retain these records in perpetuity, logically the plan sponsor, and (2) responsible party(ies) need to be diligent in reporting deletions on Form 8955-SSA. Then the too often occurring scenario from above gets avoided.