After doing a bit of tricky UV work, I tried to freeze the UVs to get rid of those green outlines in the textured decal view that show projections. Some of them disappeared; some, however, stayed. I made sure to select every object and its UVs and hit freeze, but at the end there were still six or so projections showing.

I opened up the explorer and found that they were all under one object - which had more projections which were successfully frozen, but had these left over somehow. I selected all its UVs, hit Freeze again, and the projections still refused to vanish.

I know I could hide them if I wanted, but I'm not sure if that would have the same effect in-game as freezing them - and it does bother me that the freeze button isn't working. What is going on?

Sometimes 3D applications can get a bit funky. If you froze all of the object's projections that you are going to export, then you froze them. Just because it shows the projection cages in the perspective/orthographic views doesn't mean the UV's weren't frozen. I'd just try exporting the object, and seeing if it has any problems. It shouldn't, since you said you froze each object.

AFAIK you dont have to select anything else than just the object to freeze UVs, projection control objects(green outlines in the viewport), modeling history, etc.

My problem is that I do select the object to freeze its UVs and have some of them freeze but not all. Six projections still remain afterwards and won't go away regardless of further freezing attempts. I can expand the object and there they are, under it, all selectable and certainly real - I should just ignore them?

The green outlines visible in the viewports are called Texture Supports, also hiding and freezing are two different things.

The issue you're experiencing sounds like it could be rare since I can't find any other documented cases. The only way I could almost reproduce this(in Mod Tool 7.5) was when I tried freezing from inside the Texture Editor(Edit>Freeze or ctrl+f) with a single selected object that had multiple projections. If I switched to each projection in the Texture Editor(UV>[*projection]) then tried to freeze from Edit>Freeze then it worked. When freezing the modeling construction history(Freeze M) or freezing all modes(Freeze) from the MCP it worked as it should also.

If you absolutely can't freeze the texture projections then you might be able to work around it by duplicating the object and stripping it of all projections then use GATOR to transfer the UVs from the original to the duplicate or if this is a rare problem then it isn't likely to happen again and you could just re-UV the parts that wouldn't freeze, you could use Roadkill+Roadkillplugin for XSI to do it quickly.

I have had this happen to me, I ended up just turning of the texture supports, it didn't affect any of the mapping when I exported.

Not a real answer I know. Here is a question for you and this is just a wild, I am not in front of my home computer right now theory. Are you using clusters on your model and have applied different projections to them? If you are try deleting the clusters see if that makes any difference.
Just thinking along the lines of if you apply a different texture to a cluster changing the main texture for the mesh won't change the texture for the cluster you have to select the cluster and apply the new texture there. But if you delete the cluster it will now use the main texture.

Like I said though this is just a wild theory.