The phrase "a shrinking portion of" is correct and usable in written English.
It can be used to describe a decreasing segment or amount of something over time.
Example: "A shrinking portion of the population is engaging in outdoor activities as technology becomes more prevalent."
Alternatives: "a diminishing share of" or "a declining fraction of".
White voters are a shrinking portion of the county's demographic.
"The city is still a shrinking portion of our allocation".
In addition, she said, "Smith" was keeping a shrinking portion of the audience of the two hit shows that preceded it on Tuesday nights, "The Unit" and "NCIS".
Blue-collar voters in Iowa and New Hampshire came out in force for Trump and Sanders, but, over all, they represent a shrinking portion of the electorate.
Discouraged by their career prospects if they study abroad, even at elite universities, a shrinking portion of Japanese college students is seeking higher education in the West.
Not only was "Smith" keeping less of its lead-in audience, but a shrinking portion of the previous week's viewers returned each week to see the next installment of "Smith".
Mountaintop removal mining, the only part of the coal industry the policy covers, is a small and shrinking portion of total United States coal output.
(They only provide true "insurance" in cases of catastrophic care for the young, a small and increasingly shrinking portion of healthcare expenditures).
Global manufacturing employment is shrinking, simply because of enormous increases in productivity, and America is likely to get a shrinking share of the shrinking number of new jobs.
Gross margins on that shrinking portion are an impressive 88%; services yield a less lofty 54%.
"You might make 10 per cent profit because the meat is so expensive and there's so much of it," says Sax. Shrinking portion sizes is not an option.
