Hi,
AFAIK, the raster should no longer be floating point after reclassification... if you're working in ArcGIS, are you using the Spatial Analyst "Reclassify" tool?
This *should* work:
1. Convert the ASCII to Raster (with FLOAT selected) (Conversion toolbox). You should now have a continuous, floating point raster.
2. Reclassify (Spatial Analyst toolbox). You should now have a continuous integer raster.
3. Convert Raster to Polygon (uncheck Simplify Polygons if appropriate). The class value should now be in a field called grid code... if you set your symbology to "Categories - Unique Values", and Add All Values, the color scheme should reflect the classification.
Does this not work for you?
I've uploaded an archive containing the outputs for each step of the process to my Dropbox (http://dl.dropbox.com/u/1058849/reclass_example.zip), where it'll be available short-term (bv_hot_rast -> bv_hot_reclas -> bv_hot_poly.shp). The original .asc was bradypus_variegatus_hotlayers.asc, from the Maxent Tutorial example.
John