3D Studio Max supports the export to several CAD and other picture formats - including PNG, so it is likely that you can convert ASE files to PNG using this program. There is a free trial available on the developers website.
Convert 3D Studio Max ASCII scene export data to Portable Network Graphic.
We found one software available in the database for this conversion.
Microsoft Windows software - convert ase to png on Windows
A widely-used 3D animation application from Autodesk
Convert from ase file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.