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May I have a copy of your source image? There is no such thing as a 1-bit alpha PNG unless you mean a PNG where the transparency is carried in the tRNS chunk.
P.S. you could try -sample instead of -resize.
Identify says the alpha is 1-bit even though it's really 8-bit, when the only values are 0 and 255.
The "resize" operation creates other values due to interpolation of alphas.
To get back to the 0/255 condition, use -ordered-dither command (look it up to get the exact syntax; it's something like
"-ordered-dither 2x2 opacity" but I don't remember exactly).