Hard to know since you don't say what the mix is, what kind of pots they're in & the size of the pots, as well as what kind of light (how much) they get.

I grow indoors in NYC w/dry, winter heat & I water every 2nd wk or so. Once a month sounds like too little water to me.

FYI for the future, if you're losing them but still have a couple of leaves, cut the last few leaves off, let them dry for a wk or so & them insert them dry into well-draining C&S type mix & they should re-root just fine (as long as you keep straight which is up & down from its original plant). You need not water them for a long time, just wait to see new growth & then water somewhat.

I'd suspect it's something in the mix, or that the mix has compacted & doesn't take up water.

These leaves that you say pull off w/ no resistance, are they dry & brittle (crunchy-like) or soft & mushy to the touch? Dry/brittle would suggest too little water (to me) while soft/mushy would suggest too much water. Hope this helps.

If the roots haven't rotted, you might be able to save the whole plant as is. One of my first Sans, a Hahnii with plenty of healthy leaves, broke off and toppled right over last fall. I cleaned off the stump to make sure no rot remained and stuck it a bit into the dirt in a new pot, propping it up with chopsticks. Now, 4~5 months later, it has made new roots and new leaves and is standing on its own, while its original roots, still in the pot it fell over in, have produced the beginnings of 5 new plants, the tallest one already about 4" high. The vitality of these plants never ceases to amaze me.
Re watering, I do less in the winter, though my Sans are indoors, and I never decide to water just by the time that has elapsed, so I don't know if I am doing it every few weeks or once a month. Even my different plants in different pots differ. I use one of those dry-moist-wet meters that you stick into the soil, and don't water until the meter says that particular plant is good and dry. This meter has worked for me so far.
I don't use it when the plants are outdoors in the summer, however.