Sometimes asking for a second interview may work for you, because the employer may view it in a positive light and respect your attempt. Glassdoor says:
It takes courage to request a second chance and some employers may admire that, said Tashana Sims-Hudspeth, a Columbus, Ohio-based human resource manager who also teaches on HR and being successful in college. She suggests an approach that includes an apology, a general explanation of what went wrong, and a request for a second chance. The candidate must be very clear how much they want to work at the employer and then use their personal judgment on giving a detailed explanation on what contributed to their bad performance.
If you were told that you weren't picked because another job candidate had a skill you didn't possess, Keystone Associate’s Pennell Locey says you should take a six-week class to brush up on the skill, or gain the experience through volunteering for a two-month charity project. After you've gained the knowledge or the experience, write back to the hiring manager to let them know that you have put in the effort to attain the missing skills and experience they were looking for. If you do possess those qualities, Locey encourages job seekers to write a brief follow-up email and cite one or two examples that highlight them. Personally, I think there's no harm in trying for a second chance and that the worst response you can get is a "no." As long as you go about it with finesse, reaching out to employers again might leave them with a good, and more memorable, impression of you, and they may potentially keep you in mind for future positions.