Actually the FBI keeps track of all background checks, yes they can not keep the details but they do keep that a check was run on person X at this time by dealer Z. They then find out they need to track down firearm Y that was sold by Dealer Z at a specific time, all they need to do is go back to the records for that time and they know who to contact.
I'm not sure that is true. At least not for tracing firearms. Traces are done as a series of phone calls starting with the manufacturer / importer, asking for the disposition record, and following the chain until they find the dealer that has a 4473. They ask for a copy of the 4473 and contact the buyer, and see where that leads.
As for keeping information, all they can keep now is demographic / statistical information. I'm not sure at what level, but all personally identifying information is suppose to be destroyed.
I am not saying that they follow the law. I'm not saying they aren't. But here is what they are suppose to do, according to law.
From the FBI website:
Privacy and Security of NICS Information
The privacy and security of the information in the NICS is of great importance. In October 1998, the Attorney General published regulations on the privacy and security of NICS information, including the proper and official use of this information. These regulations are available on the NICS website. Data stored in the NICS is documented federal data and access to that information is restricted to agencies authorized by the FBI. Extensive measures are taken to ensure the security and integrity of the system information and agency use. The NICS is not to be used to establish a federal firearm registry; information about an inquiry resulting in an allowed transfer is destroyed in accordance with NICS regulations. Current destruction of NICS records became effective when a final rule was published by the Department of Justice in The Federal Register, outlining the following changes. Per Title 28, Code of Federal Regulations, Part 25.9(b)(1), (2), and (3), the NICS Section must destroy all identifying information on allowed transactions prior to the start of the next NICS operational day. If a potential purchaser is delayed or denied a firearm and successfully appeals the decision, the NICS Section cannot retain a record of the overturned appeal. If the record is not able to be updated, the purchaser continues to be denied or delayed, and if that individual appeals the decision, the documentation must be resubmitted on every subsequent purchase. For this reason, the Voluntary Appeal File (VAF) has been established. This process permits applicants to request that the NICS maintain information about themselves in the VAF to prevent future denials or extended delays of a firearm transfer. (See VAF Section below.)
Now all of that is for NICS background checks. There are differences in what is to be kept for traces.