Applegate won three medals at Rio 2016 to add to her gold from London 2012, despite having career-saving surgery nine weeks prior to the Brazil Games.
But, as she has not managed a personal best this year, her funding is set to drop from £21,000 per year to £11,000.
"That means we can't continue," Applegate's mother Dawn said.
Dawn Applegate told BBC Radio Norfolk: "We just can't financially find that kind of money to carry on.
"Jess was on £21,000 but also had extra help from donations and other funding which supported everything. We just really don't know what to do at the moment."
The funding has helped Applegate pay for necessities such as travel, race entry fees and racing suits.
A British Swimming spokesperson said: "British Para-Swimming has been working through a robust performance review programme with coaches and athletes to decide who meets the UK Sport programme criteria and will receive direct support through the World Class Performance Programme.
"Over the next 12 to 24 months the sport will target support to the World Class Podium Potential athletes giving them more opportunities than ever before to help them to move up the pathway."
Four-time Paralympic medallist Jessica-Jane Applegate may be forced to retire at the age of 20 after a drop in funding from British Para-Swimming.