Hi Saucer. You're lucky your WP is flowering as much as it is...Sounds like something is lacking....a nutrient concentrating on flowers instead of leaves.
Do you fertilize? If so, what type do you use?
Living in Il, I don't fertilize succulents in winter, but since you're in SF I don't know when/if plants go dormant certain times of the yr, or the proper time to fertilize.
If it were my plant, and time to fertilize, I'd use something with a bit more nitrogen.
There may be another reason leaves are dropping..My WP doesn't drop leaves..

Saucer, when you say the leaves/stems sever, what do you mean? I know what sever means, LOL, but don't understand why it's happening..Hmm, that's a good question.
Any pets/kids? When they sever, is it a clean cut?
Older, mature leaves yellow and die back, but not newer leaves.
When they drop, do they discolor? Are stems firm or mushy? Toni

We have some emerald ripple peperomias, and some watermelon peperomias (Peperomia caperata and argyreia, respectively), at work that are doing similar things, though it's slightly different: in both cases, the petiole ("stem" connecting the base of the plant to the leaf) goes black and shrivels up, but with the caperatas, the leaf dries up too and remains attached, whereas the petioles on the argyreia get mushy and the leaf pulls itself off before the petiole gets completely black. I think the caperata version is more or less normal, but with the argyreia I suspect some kind of slow, creeping rot: the leaves otherwise look healthy, even after they've fallen.

I suspect, since you say your plant is also blooming, that what you describe is natural and nothing to be worried about, but further description, or a picture, might be helpful to pin the situation down one way or the other.

I've never seen the above described problem, sorry can't offer help.

I recently got a small cutting of this, have lost it a few times before, so am trying again. I particularly like its pretty leaf design.

Hi Toni,

Any special tips to try & keep this alove? Mine came to me in a very peaty mix that I'm a bit concerned abt. Don't know if I should switch out the mix or maybe just add more perlite. Is this is a Pep which likes to be somewhat moist all the time? Thanks!

Thanks for the responses everyone!

Toni, up until late Fall I was feeding it every other week with Miracle Grow with a shot of Super Thrive once a month. Since it's gotten colder I've slacked off on the fertilizer. I've also switched to Eleanor's VF-11, which I feed in a diluted dose once every month or two until Spring. I keep trying to treat my plants like they're dormant but most of them don't really seem to want to go to sleep! It's easy for plants to get confused around here where we have some 7 seasons a year as opposed to the usual 4!

But no, no pets or kids. What I mean by sever is that a particular spot on the stem will just sort of break down and rot, I guess? It is usually a clean cut. It's like the tissue just seperates. The huge flower on my Cattleya did the same thing after it was finished blooming. It was like someone just came by with a really sharp knife and lopped it off. The leaves are fairly healthy looking though when they drop. I will say that it hasn't happened for awhile either.

Mr Subjunctive, I'll try to get a picture next time it happens. I wish I'd taken a picture of the one that seperated in a bunch of places, that was weird.