Yes mayonnaise is considered to be a high risk food because if the mayonnaise is left out at room temperature for longer than a few hours when you open it up then it can develop bacteria that can make you sick when eaten and cause food poisoning.
As long as you keep the lid on the mayonnaise jar and refrigerate the mayonnaise after opening and use it within a few weeks to a month the mayonnaise should not cause any health issues.
But if the mayonnaise smells bad or tastes bad then throw it out to avoid risk of food poisoning from the bad mayonnaise.
When the jar of mayonnaise is factory sealed and not opened up it can last for a few months to even as long as 6 months before going bad.