Are both okay: This has been an ongoing issue starting a month ago.
And
This has been an ongoing issue starting from a month ago.
I wouldn't say those versions are wrong, but natural English is simply eg This has been an issue for the last month.
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I wouldn't say those versions are wrong, but natural English is simply eg This has been an issue for the last month.
I don't see that 'from' adds anything to your sentence. I recommend that you leave it out.
So the first sentence is much more OK than the second.
CJ