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The phrase "appear to be declining" is correct and usable in written English.
You can use it when discussing trends or changes that seem to be decreasing in quantity, quality, or effectiveness.
Example: "The sales figures for the last quarter appear to be declining compared to previous periods."
Alternatives: "seem to be decreasing" or "look like they are diminishing."
Exact(44)
Although the Little Woodstar has a moderately large distribution, it is nowhere common, and its populations appear to be declining.
Yet the numbers remain relatively small, and globally, deaths from terrorism appear to be declining, not rising.
The impact of pesticides on amphibians is of particular concern because their populations appear to be declining on a global scale.
New Ebola infections in virus-ravaged Liberia appear to be declining for the first time in months, the World Health Organization said Wednesday.
For example, levels of PCB's and other industrial chemicals appear to be declining in studied polar bear populations, as in this new paper.
Although the entire population has not been estimated, it is described as common and does not appear to be declining sufficiently rapidly to be listed as Vulnerable (BirdLife International 2013).
Similar(16)
Filmmaking appears to be declining.
But it appears to be declining.
Support for other jihadist groups also appears to be declining.
By September support for Hanson appeared to be declining.
It's not necessarily making people richer, since household income appears to be declining.
More suggestions(17)
appear to be increasing
appear to be falling
appear to be decaying
appear to be dwindling
appear to be undermining
appear to be sliding
appear to be advancing
appear to be deepening
appear to be reducing
appear to be disappearing
appear to be deteriorating
appear to be diminishing
appear to be rising
appear to be joking
appear to be going
appear to have declining
appear to be making
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com