The phrase "falling behind" is correct and can be used in written English. For example, "My grades are falling behind and I'm feeling overwhelmed."
"Just falling behind hitters.
Soon she was falling behind on bills.
But they're still falling behind".
If you are falling behind, be proactive.
"I'm falling behind in school work.
But falling behind is not always bad.
"Companies don't like falling behind," he says.
The Hurricanes won despite falling behind twice.
She ended up falling behind in rent.
Americans were falling behind, he said.
"We are falling behind," Mr. Vallone said.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK