I believe this is a sign of low humidity. Do you have a source of humidity around your plant?

Planto

From the way you talk about this plant, sounds like you've had it a long time. Has it been repotted? The roots might be out of room to grow?

Does your plant receive direct sunlight? If so, it looks like sun burn to me. These are shade plants....

Thank you all for your input here. :)

I can categorically reply "no" to each of your suggestions. The plant lives in a small shower area, so it gets plenty of moist air. I have had a it a long time, but I just repotted it last season after a bout with tiny gnat insects. (I added a layer of sand over the soil, which seems to have done the trick.) And its windowsill faces north and never gets a drop of sunlight.

I've seen suggestions online that perhaps fluoride could brown the edges, but our water supply isn't fluoridated, so I'm at a loss as to why I'm getting these brown spots. :/

raymondo17,
Okay, you have me stumped then! How about this... is it possible they're dying from old age? That's the only other guess I can come up with.

Planto

I think the sand could be 'clogging' things up, filtering down into/filling the tiny air pockets. Roots need oxygen and moisture at the same time. Is there ever water sitting in the drip saucer? Do you have a pic of the whole thing?

The same thing happened to me. Mine happened after the transplantation around October last. Actually I transplanted my plant twice. The first soil, although peat based was not that moisture retaining and the plant thrived. The 2nd soil (moisture retaining) was horrendous. It is then that I had the brown spots.
Normally the best time to transplant is spring. But the plant was looking really unhappy, with ugly leaves. I had to remove 2/3 of the plant. And then planted it in a 5-1-1 mixture (5 pine bark, 1perlite and 1 peat)
Anyway since the transplant it has been sulking, no growth at all, till now.
As purple said yours might be water logged. Mine was...

Sorry for the delay in responding. I'm thinking the only probable reason the browning is occurring may be over watering. It actually seems to be doing quite well, just the very smallest leaves are browning, while the large leaves look very happy. (Please see photo.) So I'll try cutting back on the watering to maybe once every other week and see if that helps.

Thanks!

Here is a link that might be useful:

I could also swear low humidity is the culprit.

The plant may get "plenty of moist air" in a "small shower area", but that does not equal good humidity on an ongoing basis, unless showers are taken every few hours 24 hours a day, and the door is kept closed all the time, and the vents do not work. If you have a humidity meter, measure it to find out for sure.

However, the plant overall looks very good - and those little flowers are adorable. Mine was flowering last year, but not this year for some reason.

The fact that it's the oldest leaf (looks like it) that's browning may just mean natural order of things - old leaves die and new ones take their place.

Thanks for the input, green toe. I appreciate it. The plant does look healthy these days, so I'll keep my fingers crossed. :)