Hi and welcome to the forum
Female platies can sometimes give birth to a few young and then hold off giving birth to the remaining young for a few days. This is normally caused by stress and the female doesn't like something in the area, so she holds onto them a bit longer.
If the female is gasping at the surface, that is a bad sign and could be a water quality issue (ammonia, nitrite, nitrate), or a health problem (gill issue or internal issues).
Can you post a picture of her and the entire tank, and a 1 minute video of her gasping?
You can upload videos to YouTube, then copy & paste the link here.
If you use a mobile phone to film the fish, hold the phone horizontally so the footage fills the entire screen.
Is the female eating well?
What does her poop look like?
How long has the tank been set up for?
What is the ammonia, nitrite, nitrate and pH of the water?
How often do you do water changes and how much do you change?
Do you gravel clean the substrate when you do a water change?
Do you dechlorinate the new water before adding it to the aquarium?
What sort of filter is on the tank?
How often and how do you clean the filter?
What other fish are in the tank with her?
How many babies did she produce the other day?