Sorry for replying so late to this thread.
Thank you for all the input.
I was certain it couldn't be a texture problem, because I could see that the candle texture I was using had the drips visible there. It didn't occur to me that it might be a uv mapping problem, or whatever.
Anyway, a friend sent me over the texture he uses for his candles, and as soon as I popped that in the requisite folder, boom, they were back again. Problem solved.
I had been using Ruins Clutter Improved. I had no candle meshes in any of my folders though (apart from horn candles, which weren't a problem to begin with). Textures, however, I had them, and like I said, replacing them with someone else's worked. I'll have to find out which textures they were using.