Joe,
There are so many things that can cause this from genetics to "sometimes it just happens" (okay, there would always be a reason, but sometimes you just can't identify it). Could the leaves be too close to the cold window? I would think the heat (within reason) would help at this time of year.

I would cut off the brown tips and swab the cuts with peroxide. I might also begin experimenting with cultural changes, as in give this one less fertilizer or move it away from the light. Perhaps, someone else has other suggestions.
Any chance you have a photo?
Gail

it took me long enough to get my act together. I can't figure out if I can put in multiple links; I have a few pictures of the plant but they are dark, and it is the same thing. I moved the plant out of any direct light and the new leaves are not browning, so I suppose that was it.
Joe

Here is a link that might be useful: browning leaf tip