The issue is, in part, what objective evidence is there for or against her "forgetfulness." If her productivity is down, forgetfulness may or may not be a reasonable conclusion depending her job duties. If she is a blue collar worker who works with her hands, it may be less likely than if she is a manager or scheduler, etc. If there are specific instances with reasonably substantiation where your mother has forgotten items, those instances may support management's theory
If management is acting in bad faith, or is unreasonably misjudging her work performance based on stereotypes of older workers, then in theory management may be sued for age discrimination. The details matter greatly. Arguably it would be safer for management to fire her for missing productivity outright than to try to speculate as to what the cause is.
If she is fired, she should definitely consult with legal counsel. But the "devil" is in the factual details. Good luck to you and to her!
There is no easy answer to your question. The comments appear to be ageist, but they may have some basis in reality. Your Mother should document her performance, all comments and criticisms made and confirm verbal interactions by email or memo whenever necessary. Documentation will assist her in defending herself and/or challenging any adverse employment action.
The Supreme Court raised the bar in proving age discrimination. If your Mother is terminated or demoted, she had to prove that "but for" her age the employer would not have taken the challenged personnel action. In effect, she must establish that age was the determining factor underlying the employment decision. Juries tend to look through the subterfuge, but judges tend to find numerous ways to take the decision away from the jury.
There is also the likelihood that the employer will seize on a pretext -- make up something or blow something out of proportion -- to justify its actions. To prove pretext, your Mother will have to show that younger employees in a similar situation were not treated the same way or demonstrate convincingly that the allegation is made up or exaggerated beyond all proportion. Similarly, it may group her into a layoff and claim that it was reducing its work force.
One obvious piece of advice is for your Mother to start looking for work while she is employed and to do everything possible to try to forestall further criticism. The situation is difficult in this economy irrespective of age. Employers tend to cherry pick in hiring and get rid of perceived dead weight with or without a good reason. Employers often are able to hire younger and/or desperate workers for a lot less money. I am trying to provide a reality dose.
I am not anti-employer. There are employers who are bad apples and there are employees who do not pull their weight. There are also genuine victims in the workplace. The problem is that litigation is time-consuming and expensive.