... One native English speaker says
"He is resembling his father more and more as the years go by."
would be correct. It's from this page:
"Resemble" can't be used in progressive form?
...
Good find! But I still don't think "more and more..." improves it enough to make the "is resembling" acceptable. (E.g., I'd suggest alternatives (alternative wordings) if I rec'd it on a student paper.)
Some other comparable verbs in the same sentence sound better to me than resemble. (add "more and more as the years go by" or something similar to each)
He takes after his father ~
He is taking after his father ~
He looks like his father ~
He is looking like his father ~
For the last pair it seems to sound better if the "more and more" is moved:
He looks more and more like ~
He is looking more and more like ~
***
Some of the examples in your link sound okay:
1. It's looking more and more like it's going to rain.
2. As I read that novel, {I find that} I'm liking it less and less.
3. The mixture [is] smelling sweeter and sweeter as it warms up.
1 and 3 are acceptable. 2 sounds like a modern (millennial?) usage.
You can use google to get a sense of how common a word string is. (hits) Though not all of those hits are in the particular grammatical context at issue here, I think the sheer lack of hits for "is resembling" does reflect how rarely it is used in the progressive, and how much its grammatical usage differs from other verbs/expressions that I might offer as a better phrasing of the same idea.
"is resembling" (46,300)
"is taking" (102,000,000)
"is looking" (208,000,000)
"is smelling" (258,000,000)
"is liking" (416,000)