There may be a more elegant approach, but this is one solution...
* Assuming your raster cells are discrete values (e.g., integers, classification). Also assuming that the raster isn't huge.
1. Convert the raster into polygons (Make sure "Simplify Polygons" isn't checked)
2. Once you have your polygon feature class - run a Dissolve based on the values (Do not create multipart features)
3. Create a new field and calculate area in sq. ft.
4. Select by attribute for areas >50 sq. ft.
Done! But, if you need to go back to a raster for further processing (e.g., masking) ...
5. Create a field in the dissolved polygon feature flagging the polygons that are >50 sq. ft (e.g., those areas = 1, all others = 0)
6. Dissolve based on that field (Again, do not create multipart features)
7. Convert polygon to raster based on that field. (Make sure you set the raster cell size to 1 m, and set the Raster Snapping in Environmental Variables to the original raster, so that the pixels line up)
Good luck!