While milder cases heal relatively quicker, and could possibly have less strengthened immunity and waning antibodies after a while, it is also said that milder cases are more at risk for reinfection since the level of antibodies mounted could be lower, and hence, less protective by default.
This has been proven by some anecdotal evidence as well as case studies. Some preliminary research has also indicated that while even a mild COVID-19 bout could cause immune changes, the level of antibodies mounted post infection could be determined by the severity of the fever. Higher the fever, higher could be the antibody response and vice versa. This, primarily, could be the reason why milder cases may see lesser antibody production in comparison to a severe COVID patient- leaving scope for reinfection.
Similar risks exist for those who have barely noticeable, asymptomatic COVID infections.
However, do remember that while experts gather more data on the nature of infections, interpretations may also change. As studies have shown, even some mild COVID-19 cases could mount lasting immunity, while some do not. Therefore, the matter is subject to a lot of factors and health risks.