Same here. All sizes, positions are remembered for all individual modern skins (settings saved in studio.xnf)
If you're using scaling to resize windows, as opposed to just resizing them, then you need to checkmark "locked" instead of "temporary" (Menu > Windows Setting > Scaling).
Apart from that, sure, it could be some settings need adjusting in:
Prefs > Modern Skins > General/Alpha Blending tabs....
Or it could just be that Winamp isn't exiting properly, and therefore settings aren't being saved.
Remove any potentially dodgy 3rd-party plugins and/or try a clean install
Maybe also try installing to a new dir
Though to be frank, it is very difficult for us to diagnose such problems without knowing any of your system specs
or what other software is concurrently running....