You can't prove a negative, so they can't be convicted of perjury for lying about whether they remember;
Yes, they can. The government can convict the witness of perjury by proving that they did remember. This may be difficult, but it's not impossible.
Now you may say that we can't ever prove with certainty what a person did or didn't remember. But the legal standard isn't certainty, it's beyond a reasonable doubt. So a jury is allowed to draw a reasonable inference about whether they remembered, based on evidence of their outward behavior and other circumstances.
As an extreme example, suppose Alice was overheard chatting freely about topic X an hour before the trial, but when asked about topic X on the stand, said she didn't remember. When presented with evidence of her earlier conversation, a jury could reasonably infer that she was lying about not remembering. Is it possible that she truly had a memory lapse in the intervening hour? Sure, anything is possible. Is it reasonable to believe that she did? Probably not.
The US Department of Justice's Criminal Resource Manual has this to say on the subject:
Witnesses who claim not to remember, rather than deny a fact, may be prosecuted for perjury. However, the government must prove both that the witness at one time knew the fact and that the witness must have remembered it at the time he or she testified. United States v. Chen, 933 F.2d 793, 795 (9th Cir. 1991). If the dates of the transaction and testimony are sufficiently close, memory may be inferred. Instances in which the witness remembered other events that occurred at the same time or earlier than the event in question, or mentioned the event either immediately before or after his testimony, would be probative of the witness's memory at the time of the testimony. The two witness rule does not apply to prosecutions based on false memory lapses, and circumstantial evidence is sufficient, since there is no direct evidence possible concerning what the defendant actually believed. Gebhard v. United States, 422 F.2d 281, 287 (9th Cir. 1970).
There's a similar issue in all laws that deal with a person's knowledge or intent. Suppose Alice hits Bob with a stick and he dies. To convict Alice of murder, it must be proved that by hitting Bob, she intended to kill him. Can we ever really know what was in her heart? Maybe not, but if there is evidence that shortly beforehand, she told someone that she was going to kill Bob, it would be a reasonable inference that this was her intention.