I think we'd need to see the file, as I've just opened a .osm file in version 4487 without any problems (on Windows 7). Pastebin it somewhere, perhaps?
Alternatively, download an area in JOSM, save this as a .osm file and see if it can then reopen it, to try and see whether the problem is with your other file(s).
In case it makes a difference, the .osm file I opened was created using Osmosis cutting a polygon area out of a Geofabrik extract.extract. I have just repeated the test by downloading an area, saving as .osm, quitting JOSM, restarting JOSM and loading the .osm file without problem.