Multiple handgun purchases (two or more) within a 5 business day period from the same FFL requires the FFL to fill out an ATF Form 3310.4 and send it in. Those are tracked by the ATF to insure the buyer is not doing straw purchases.
They barely have the manpower or resources to do even that.
Here's the reality, folks. The 4473 forms are kept on the dealer's premises. If they are turned over to the ATF, they go to a warehouse in West Virginia for storage.
There, they sit in that warehouse in boxes. Hopefully, the dealer kept them in some sort of order when he sent them in. Probably not. (Some dealers soak the forms or deface them in other ways before relinquishing them.) In any case, the ATF is forbidden from collating them or entering them into a database. There's just boxes upon boxes, thousands of them, sitting in stacks.
Imagine having to do a trace under those circumstances. The agent would have to find Jim Bob's Firearms' boxes, extricate them from the stack, then go through the boxes manually, looking for the right form. Even legitimate traces are a logistical nightmare.
Of course, that assumes that the form is still there, and that the Jim Bob kept his books straight. The idea of even starting a database from that is very daunting, and the execution would be impossible.
As far as NICS, they don't know what gun (or guns) are on the form. They're only told "handgun," "long gun," or "other." Even that data is removed 24 hours after resolution.
Now, somebody's going to come along and claim that there's a super-secret conspiracy, and that the information's being kept. Let's think that one through. Our government can't keep stealth bomber designs and arms-smuggling schemes quiet for long. Would they really do a better job of enacting a covert nationwide firearms database without people finding out? Doubtful.