Only one valid NIF root node is loaded from a single file
A NIF file may define multiple valid root nodes that are then added into the scene graph as children of the actual "root" node. OpenMW 0.46.0 currently only uses the first entry of the relevant list (and discards the entire file if it's not a valid record) while the current OpenMW (in-dev 0.47.0) picks the first valid entry of the relevant list and discards the rest of the records. Either approach causes problems when a model doesn't wrap all of its usable nodes into a single root node and isn't consistent with how the NIF file may end up looking in Morrowind itself or in, say, NifSkope.
The theoretical solution would be to add a wrapper node that every valid root node is attached to, it can be optimized out if there's only one valid root node like in most of the situations.
If I recall correctly one real-life test case is the one mesh from this archive (courtesy of Shehriazad) which doesn't have a "new" suffix. Most of the model's contents will be invisible in OpenMW due to the issue in question. InvisibleVSVisible.7z
I think it comes from this mod.