What a browser can play
Every web browser ships its own audio decoders, and they cover the web's formats: MP3, AAC and M4A, Opus and Vorbis in Ogg, FLAC and WAV. WMA was never one of them. Its codecs are Microsoft's, and no browser added them.
So when a web page offers to convert a WMA file, one of two things is true: the file is being sent to a server that does the work, or the page cannot actually do it.
Why Morph can't convert it for you
Morph converts on your device. The file is read and written again inside your browser tab, and it is never uploaded. That promise has an edge: a format your browser cannot decode is a format Morph cannot read.
We would rather tell you than take your file somewhere else. When you place a .wma file on Morph, it says so straight away, before you wait for anything.
What to do
Two more ways back. If the WMA came from a CD you still have, rip the CD again as FLAC or MP3. If a device recorded it, such as an old voice recorder, its desktop software can usually export MP3 or WAV.