Succulents falling apart
I'm quite new to growing succulents (and even newer to this forum) and I'm in need of some help so I can save my plants.
I have a small bunny ears cactus I bought from Lowes about 6 months ago, and a coppertone sedum I purchased at a local plant sale about 3 months ago. Both have been doing very well until about a week or two ago.
The cactus recently began dropping pads. It had grown several new pads since I brought it home, and most recently several tall, thin, light green new growths spouting straight up out of the pads. About a week ago pads began falling off. At first I thought they were too heavy with the new growth because I found three had fallen off while I was at work one day, but then I accidentally bumped the table where the cactus is growing and more fell off! They don't appear to be rotting and overall look very healthy. Why is this happening to my cactus, and can I regrow the pads that have fallen off?
My sedum has a similar problem, except I'm noticing some of its leaves are shriveling up then falling off, although others (seemingly healthy) fell off when I bumped said table.
I water both plants less than one time a week with a couple of table spoons of water. I try to be careful not to over water, although I've read that underwater causes succulents to shed parts in order to save the plant as a whole.
Any advice you can provide would be very welcome. I love having these plants in my home and would like to take the best possible care of them I can!