The issue I was having was that when I would walk through a certain hallway in my map, the server would crash.
Using the "Entity Report" tool, I came across some brush entities (specifically, a couple of func_doors, a couple of func_brushes, and a trigger_multiple) which didn't have any actual brushes associated with them. I was going through selecting each of the entities in the Entities list, refocusing on each entity (for reasons unrelated to this issue), when I noticed that some of them had their origin point appear on the grid yet there were no brushes hi-lighted. These origin points were located right in the middle of the hallway that would crash my map. I deleted these entities, recompiled, and the map no longer crashed.
I'm not exactly sure how it happened, but I think these brush entities lost their geometry when I attempted to delete the entity with ignore groups turned on, and it ended up only deleting the brush but leaving the entity itself. Or something. I dunno.
Anyway, I suspect (but cannot confirm) that the crash occurred when the doors attempted to "open", but not having any actual geometry to move, the game engine instead went kaput. Or maybe because the trigger_multiple didn't have any actual geometry, touching its origin point makes the game engine go kaput. I'm sorry I can't say for sure. All I know is that once I removed these entities, it stopped crashing.
Also, this may or may not be relevant, but these were entities that I had created in previous versions of my map, and then later deleted (or attempted to delete, anyway). Some of these old entities shared some names with new entities that I had created elsewhere in the map. Perhaps the crash is related to a name conflict that makes the game engine go kaput when the old entities are somehow triggered.
I hope this helps somebody. It sure frustrated me for a long while.